Muktol

[[Goblin Fireslinger]] was the only common I was able to find that would suite in here. I was looking for something that could deal damage to player or creature, but those where all cmc 3+. [[Flame Jab]] with Retrace could be an option, or [[Lava Dart]] with flashback
Something like [[Fable of Wolf and Owl]]? Only problem is that they are all uncommon or higher.

I finally had the time to do some testgames (results see above) and thus did some changes to the deck and added a (small) sideboard.
Basically the star of the deck is [[Raid Bombardment]], while [[Wildfire Elemental]] is a sidekick, still useful but not nearly as potent.Through the Bombardment you can deal a good amount of damage per turn by only attacking, and the creatures will additionally deal damage.

What about [[Fierce Empath]] or [[Mwonvuli Beast Tracker]] to tutor your heavy hitters?

Another card that just came to my mind would be [[Fierce Empath]]. This would allow you tu play your 6-mana creatures as 1-offs, as it would enable you to search for it. Another option would be [[Mwonvuli Beast Tracker]]

+1
Personally I would drop [[Hydra Omnivore]] and [[Whiptongue Hydra]] to make the deck modern-legal. You someday might want to take the deck to a local tournament and can't use it there, because of those 2 cards.
I would also try to remove some of your cards, to get the deck down to 60-64 cards.
I would definitely add some spells to protect your [[Phytohydra]] + [[Pariah]] combination, else s simple [[Doom Blade]], [[Unsummon]] or [[Oblivion Ring]] will put an end to your creature.
As for the ramp: [[Arbor Elf]] and [[Utopia Sprawl]] can generate you 4 mana T2.
Some additional suggestion:
[[Managorger Hydra]], [[Primordial Hydra]], [[Khalni Hydra]], [[Aspect of Hydra]], [[Harrow]]

https://magic.wizards.com/en/game-info/gameplay/formats/pauper

+1
[[Biomancer's Familiar]] comes to my mind, when seeing the costs you have to pay to get creatures monstrous, but it needs blue and thus is out of your current colour-combination. [[Simic Ascendancy]] would be another of those out-of-combination cards.
[[Corpsejack Menace]] (or even [[Winding Constrictor]]) could be worth a look to increase the efficiency of the monstrous ability's.

What about [[Waste Not]]? Only works when your opponent discards something, but with 14 discard options this could work out.

+1
Personally I would rather use [[Brighthearth Banneret]] instead of [[Smokebraider]].
If you want to use a planeswalker then [[Koth of the Hammer]] could be worth a look.

[[Empyrean Eagle]], [[Infernal Kirin]], [[Nether Traitor]],
[[Essence Flux]], [[Midnight Haunting]], [[Lingering Souls]],

Not a vampire but [[Hooded Blightfang]] could work well here with all those deathtouch creatures.
Personally I'm not a big fan of loosing a legality by using a single card, like [[New Blood]] here.You might want to go on a local tournament one day and can't because of this single card. Or worse, you start playing and get thrown out because you did forget to remove the card on time.

[[Radha, Heart of Keld]] doesn't allow you to play additional lands, like [[Azusa, Lost but Seeking]] does. So when you have 1 Azusa on the battlefield, you can play 3 lands in total.
[[Scapeshift]] could be an idea here, and personally I'm a huge fan of [[Harrow]]/ [[Roiling Regrowth]] (or [[Khalni Heart Expedition]], if you prefer enchantments) in landfall decks. [[Cultivate]] would be a slower, but more recent version of this card.

No, I didn't lose a bet, I simply wanted to try to make an old-school Fungi deck :)
I have once played in Arena against a deck with [[Tendershoot Dryad]], and honestly, it was not funny, as the white lifegain deck I did play back then did have some removal, but not nearly enough.
[[Sprout Swarm]] was in the starting-list of the deck, but I simply forgot about the convoke ability of the card and calculated that it would come cheaper to generate tokens with [[Slimefoot, the Stowaway]]. So I will add [[Tendershoot Dryad]] and [[Sprout Swarm]] again.
Regarding the original idea of Fungi with spore counters [[Golgari Germination]] and [[Fungal Plots]] have one big disadvantage here: They need a creature card in my graveyard. But each Fungus that you loose, looses you counters, and the ability to generate tokens.

It does, but a playset would also nearly double the price with 10$ (Mid Value)/ piece.
That's the reason why I'm building mostly pauper/ budget-decks: Because I'm only using cards that I have in my collection or that I would be willing to trade/ buy (Most of the time that is, there will surely be some deck's where I have forgotten about this rule ;) )

[[Primalcrux]], [[Doubling Chant]], [[Aspect of Hydra]]
[[Utopia Sprawl]], [[Arbor Elf]]
Hydra Deck

First of [[Deftblade Elite]] won't take out anything valuable if you don't give him deathtouch or you have [[Coat of Arms]] on the battlefield...which you have only as one-off and no way of tutoring for it.
Second, you don't have any means of casting [[Presence of Gond]] when a [[Blood Moon]] or anything similar hit's the table, so I would recommend adding a few Forests and some searchlands ([[Evolving Wilds]] etc.)
The question is: Why play defensive, when you can overwhelm you opponent with infinite warrior tokens from the [[Midnight Guard]]+[[Presence of Gond]] combo? If you want to control your opponent during your attack the you could take a look at [[Odric, Master Tactician]].

The series reminds me a little bit on the 8th edition intro decks:
https://magic.wizards.com/en/content/core-set-eighth-edition-intro-pack-decklists
(The decklists can be changed by clicking on the upper one of the deck-name and selecting the appropriate one)

two rectangular brackets on each side: [[CARDNAME]]. Tough this doesn't work for cards with an apostrophe in their name

Probably [[Rile]] or [[Thunderherd Migration]].
With [[Rile]] you will loose a cantrip thah grants you trample as one-time effect, while [[Thunderherd Migration]] already has [[Ranging Raptors]] as possible replacement in the deck.

Tilonalli's Crown could be of interest here.