Muktol

Personally i would opt for [[Soaring Thought-Thief]] with [[Malevolent Hermit // Benevolent Geist]] as sideboard replacement. Tough I'm more a pauper player, so my opinion might not be worth that much ;)
[[Relic Golem]] or [[Vantress Gargoyle]] could also be worth a look.

Sadly [[Nephalia Drownyard]] isn't legal for pioneer any more, this would be a good addition. [[Codex Shredder]] would be a weaker option that would allow you to mill continuously. Library manipulation could be done using [[The Biblioplex]]

Personally I would (re)move 2 [[Hero's Downfall]] into the sideboard and add [[Cast Down]] instead, and switch when playing against decks with high legendary or planeswalker count.

Some suggestions without knowing the original deck or what you changed:
[[Gitaxian Probe]] is banned in pauper (https://magic.wizards.com/en/banned-restricted-list). [[Clairvoyance]], [[Peek]], [[Ingenious Thief]] or even [[Glasses of Urza]] could be an option to replace it.
[[Murder]] and [[Victim of Night]] could be replaced with [[Cast Down]], [[Evolving Wilds]] could be replaced with one of the new Streets of Capena search lands: [[Maestros Theater]] or [[Obscura Storefront]]

A deck description would be a nice addition to the deck.

[[Liliana's Elite]] or [[Persistent Specimen]] instead of [[Foul-Tongue Shriek]]?
[[Evolving Wilds]] could be replaced with [[Maestros Theater]]

Other suggestions:
[[Makeshift Munitions]], [[Body Dropper]], [[Kathari Bomber]], [[Myr Servitor]], [[Hordeling Outburst]], [[Font of Return]], [[Blood Fountain]]

- [[Gemhide Sliver]] + [[Hive Stirrings]]?

When working with +1/+1 counters [[Grateful Apparition]] can do a real good job, either as carrier or as proliferate engine.

I don't think that any effect, that changes land types, that is on the battlefield before a [[Blood Moon]] enters the battlefield, would work. This is because of the layer system (https://magic.wizards.com/en/articles/archive/layer-system-2009-11-05).
A non-basic land enchanted with [[Nylea's Presence]] will still e a Land - Mountain after a Blood Moon hit's the board. The only thing that could work around this would be to enchant a basic land with Nylea's Presence because then Blood Moon wouldn't work.
From what I've seen most modern decks that fear a [[Blood Moon]] use fetch lands and the least number of basics to cast everything they have. When playing against a deck that uses Moon or is known to do so, they fetch those basics as fast as possible.

[[Gargos, Vicious Watcher]], [[Hydra Broodmaster]] for that excess mana produced by [[Mana Reflection]], [[Aspect of Hydra]] for flavour style
I would replace [[Nature's Lore]] with [[Rampanth Growth]] or any simple, modern legal, ramp spell, to get the legality to modern.

Had to google this up myself, because I'm not really firm on timestamp questions... which is exactly what is applied here.

This will only work if you're able to play a [[Prismatic Omen]] AFTER a [[Blood Moon]] entered. Both effects are applied at the same time and since you cannot decide when to put a changing effect on the stack, the so called timestamp order gets to work.
If you played a [[Prismatic Omen]] and a [[Blood Moon]] enters afterwards, the effect from the Omen will be carried out first, followed by the Moon effect. So you will first have lands that are every type, followed by lands that are only Mountains. If an opponent played a Moon first and you somehow managed to get a Omen on the battlefield afterwards, it's exactly the other way round, first only mountains then all types.

Cards like [[Nature's Spiral]], [[Reviving Melody]], [[Rofellos's Gift]] or [[Season of Renewal]] could help you to reuse [[Frogify]]/ [[Kasmina's Transmutation]]

If you can squeeze it in then [[Nylea's Presence]] could solve your Domain and land problems.

Why only 3 [[Alpha Authority]] and 3 [[Rancor]]? [[Alpha Authority]] is a must-have, unless you have something to a large number of enchantments back from the graveyard and [[Rancor]] serves as cheap target for [[Gatherer of Grace]] to sacrifice and protect itself.

Personally I would remove/ sideboard [[Valduk, Keeper of the Flame]] because with [[Champion of the Flame]] and [[Stangg, Echo Warrior]] you would have 10 cards that hunger for enchantments, which might be too much.

[[Frenzied Rage]] could be replaced with [[Madcap Skills]]

Further suggestions:
[[Call of the Full Moon]], [[Abundant Growth]], [[Kruphix's Insight]]/ [[Commune with Spirits]]/ [[Commune with the Gods]], [[Keen Sense]], [[Helm of the Gods]]

Thank you for your suggestions.
The original deck was built for legacy/ vintage legality, but with this deck I wanted to see if a Stuffy Doll deck was doable in pauper. I did look up all the cards, for safety reasons on MTGVault, Scryfall and MTG Gatherer, but sadly none of them is pauper legal.

[[Coalhauler Swine]] isn't good, because it's expensive as hell (CMC), the only good thing is that it's body means it's Bolt-proof... and it's the only card available in Pauper that has a [[Stuffy Doll]] effect.
Before [[Take Up the Shield]] was released (Just in time I have to say) the deck was even more clunky. [[Lifelink]] is a survivor from that time, but without [[Take Up the Shield]] it meant I would have to draw and play a [[Coalhauler Swine]] + [[Lifelink]] or a similar effect + [[Guilty Conscience]] + [[Blacksmith's Skill]] or something similar.

Cards from a stompy build would fit in here: [[Cloakwood Swarmkeeper]], [[Bayou Groff]], [[Hunger of the Howlpack]], [[Rancor]]

[[Flamerush Rider]], [[Breakneck Rider]] (Tough it doesn't ride any more as Werewolf. Wonder what happened to the horse and where he gets a new one when transforming back into the rider ^^), [[Smogsteed Rider]].
Personally I love the "new" search lands from Streets of New Capena because you get a mana fixing due to the land search, remove a land from your library that you can't draw later on and gain one life. [[Riveteers Overlook]] be the fitting one here.

[[Ardent Recruit]], [[Auriok Sunchaser]]
[[Emerge Unscathed]], [[Honed Khopesh]], [[Short Sword]], [[Cobbled Wings]]
And your decks could need a deck description

I can understand that you like the card, and I know that I tend to streamline decks too much, still I would like to point out why I see problems with [[Undead Alchemist]]. :-)

I haven't looked through your entire deck but in general options that allow you to repeatedly bring back creatures from the graveyard are rare and you might want to use them on other (?better?) targets. Also many decks use the graveyard and something that's stops them from doing so has "KILL ME" writen all over it. Normally one of the premade commander decks is centered around the graveyard in one form or another.

The other thing is efficiency. I know that commander or highlander decks shouldn't (only) be judged by this, but it is still an important thing to look at.
Let's say you have dealt 38 damage to a single player while [[Undead Alchemist]] is on the battlefield when someone suddently manages to kill your [[Undead Alchemist]] and you have no chance of reviving him. What happens is that you basically have dealt 38 damage, which is a lot, for nothing. Yes you reduced his library, but 38 out of 100 isn't threatening, while 38 out of 40 means you can sneeze and the player will be out of the game.

I honestly didn't think of that. Well, another thing learned ;)

Two additional suggestions that came to my mind:
[[Kasmina, Enigmatic Mentor]] and [[Davriel, Rogue Shadowmage]]

[[Lonely Sandbar]] or [[Barren Moor]] could be used as cycling lands.
Why did you use [[Mistvault Bridge]] and not e.g. [[Choked Estuary]] or [[Dismal Backwater]]? I couldn't find any benefit for an artifact land, only reason I can think of would be against land destruction due to being indestructible.

[[Poppet Stitcher // Poppet Factory]] would allow you to re-use [[Wilhelt, the Rotcleaver]]'s ability as the tokens lose all abilities (Decay), thus can attack and block and be reborn through Rotcleaver. [[Army of the Damned]] anyone with this combination? ;)

Personally I would reduce the mill part, keep only things that bring you advantage (like [[Jace's Mindseeker]]), and focus on the zombie part.

There are some cards that specifically strengthen legendary creatures:
[[Heroes' Podium]], [[The Circle of Loyalty]], [[Day of Destiny]]

[[Avacyn's Memorial]] (1$-6$) makes legendary permanents indestructible.
[[Robaran Mercenaries]] gets all abilities from your legendary creatures.
The flip planeswalkers from Magic Origins could be worth a look: [[Liliana, Heretical Healer]]
[[Teshar, Ancestor's Apostle]] or [[Yomiji, Who Bars the Way]] can help you to get some legendaries back from the grave after a board wipe.
[[Tatsunari, Toad Rider]]

Access to blue would be a cool thing, so you could add [[Leyline of Singularity]]. But sadly this doesn't fit your commanders colour identity.