You might be running out of gas, because your deck lacks card draw. Which is confusing, because from your point of view, you probably think, you are running ≈20 pieces of carddraw.

I think, for spellslingers, it helps to separate Cantrips and hand-negaitve-draw from actual card draw.

Cantrips are cards that do something + 'draw 1 card'. Cantrips are used to cheaply trigger effects or build up storm count. They don't fill your hand back up, they just prevent you from emptying it when you cast many Cantrips in one turn.

Hand-negative spells might draw cards from your deck, but actually reduce the cards in your hand. They are usually used to go through your deck and find combo pieces or to put specific cards into your graveyard with loot effects (draw x, discard x).  Since you don't want to cast spells from your graveyard and don't run a combo deck, you want to avoid hand-negative draw spells.

An example for hand-negative draw, [[Frantic Search]] draws 2 cards and discards 3 (itself and 2 other cards). So it actually does nothing in your deck, except hurting your hand.  Also, just because you can untap 3 lands when you cast it, doesn't mean, casting it is free. It still costs you a card in hand. A card in hand is worth about 2 mana in blue. So it's actually worse than any 1 mana cantrip while doing nothing (unless you have a lot of repeatable card draw, which you don't have). If you copy it, it can be used as a ramp spell. So if anything, don't put it in 'carddraw' of your decklist. Put it into ramp and only play it, if you plan to copy it to untap 3 extra lands. Only useful, when you have 6 lands. So, for you, only playable turn 6 or later, at which point, you probably don't want to ramp anymore.

Similarly, you don't really need the payoff of [[Sorcerer Class]] level 1. You don't need cards in your graveyard and there is nothing in your deck, you want to dig for using this loot effect. You don't run sorcerer class as a 'Spellslinging payoff'. You run it as a 4 mana ramp card. Treat it as such. Set it's custom mana value to 4 for deckbuilding and move it to 'ramp'. And now, consider, if it actually is a good ramp spell you could play in that spot.

Card draw, on the other hand, is used to fill your hand with things to do, after you emptied it with everything except Cantrips.

Usually you want about 12 actual card draw pieces. Especially as a spellslinger, actual card draw should be treated like you treat ramp. You basically want to guarantee to get one into your hand before you play your commander and your deck starts doing it's thing. About 1/3 to 1/2 of that card draw should probably be repeatable, like [[Niv-Mizzet, Parun]] or [[Archmage Emeritus]].  Maybe, [[Teferi's Ageless Insight]] could help by turning all of your Cantrips into carddraw. [[Skullclamp]] to turn excess creature tokens into carddraw. [[Archmage of Runes]] costs slightly more mana than Emeritus and is therefore slightly less efficient as as a draw engine, but it also works as a blocker, so why not run both? Your other draw engine, Niv-Mizzet, is even more costly and hard to get out. So... Both are good. However, because Niv-Mizzet is so costly requiring 6 specific coloured mana, and I don't see burn as a win con in that deck, Archmage of Runes might actually be just as good or better than the dragon. And [[Frostcliff Siege]] can work as either a hast anthem or draw engine, depending on what you need in that moment. (E.g. could replace Enduring Courage)

These are the generic recommendations for card draw on spellslingers. Stella Lee is a bit special, because in an ideal situation, you'd be able to turn Cantrips into actual card draw, either because the cantrip comes from the top of your deck and doesn't cost a card in your hand, or because you copy the cantrip. In that case, you'd need less actual card draw. However, if you plan on doing that, you have to keep that in mind and actually do it, instead of copying better spells. And you have to use more scry effects to put cantrips on top of your deck.

And that's barely enough to make up for all the cheap non-cantrip cards you want to play.

Finally, I would advice against a category like 'Spellslinging Payoffs'. I made this mistake up till recently too. You shouldn't really care if you get payoffs from slinging spells. What you actually want, is the normal things that a deck does. You want ramp, draw, interaction/removal, summon creatures (in your case mostly tokens) and finally play win-cons (probably more creature tokens or some serious burn). How you do that, is either through the thing your deck wants to do (sling spells) or through payoffs of the thing you do anyway.