RisenDeep

The deck is illegal because of Gitaxian Probe still banned in all formats except Vintage from the official banned/restricted list on https://magic.wizards.com/en/game-info/gameplay/rules-and-formats/banned-restricted

Adaptive Automation and/or Metallic Mimic could boost your deck even if they aren't Gnomes technically

Remand is expensive as you already mentioned, so if going into a more expensive build, I strongly recomend for
- Remand, as an alternative to Mana Leak
- Spreading Seas, to down-block some of your opponents important lands
- Psionic Blast, as a maybe removal
- Hurkyl's Recall, for Affinity/Artifact hate
- Jace, the Mind Sculptor, at least as a one drop as additional Win-Con and control card

Good point, Mausoleum Wanderer could be a good example here. It is (or I just think) cheap and can counter additionally for 1+ mana

27 Islands seems a bit overwhelming to me. You could add some lands that will value for example Faerie Conclave

Don't think of Humans or other tribes. I played a very long time well with this
https://www.mtgvault.com/risendeep/decks/merfolk-26/

and had also many Human decks as opponents and it performed well at every time. Focus on your own aggro and return dangerous creatures back to their hands or Dismember them.

You could also go for a splash and either Blood Moon their mana base
https://www.mtgvault.com/risendeep/decks/merfolk-4/
- or use some Chalice based counter control variant like these
https://www.mtgvault.com/risendeep/decks/merfolk-23/

Don't play Damnation in a creature aggro based deck, thats suicide

In formats like Legacy or Vintage, you get screwed before you could cst anything of your "combo". There are way more effective ways to get Banefire cast for example Pili-Pala<>Grand Architect Combo. Play for safety using Ensnaring Bridge and get your win-con completed behind your walls, then you have at least a small chance to win a game

You need to seperate this answer in two parts or it isn't correct. Creatures with Indestructable don't mean they don't die. They don't die to damage dealt to them but decreasing there thougnes to zero is still possible to remove them from the board

"So Tuvasa. Not really the Bant Merfolk we wanted but.... is it the one we needed.
So Merfolk running White provides much needed support that Merfolk really need."

Sygg, River Guide would make a far better job than Tuvasa ...

In Dominaria arrived Adventurous Impulse for just a single {G} for faster gameplay than the CMC 3 from Lead the Stampede

Get rid of River Sneak, really! There is an alternative from Shadowmoor; Inkfathom Infiltrator is unblockable with a 2/1 body that isn't depending on you playinf Merfolk spells all the time

Playing a lot of one mana drops isn't really successfully, you leak of good supporter cards.
Deeproot Elite is near useless in modern format because before you play your first spell that could profit from, it would see a bolt or something else. Even a Goblin could kill him at instant speed. Same for River Sneak, that will see gain if you frequently play other Merfolk only so nothing to hit here too.

If you want to go for a budget list, first think for a bunch of Cursecatcher as for the reason that it could counter some of the stuff you might get rid of and so keeps slots open for other stuff. Cursecatcher costs not even 1$ thank to Masters 25 series.

Lord of Atlantis and Master of the Pearl Trident are all arround 5$ each so those are your most expensive gains here. The cheaper alternative Merfolk Mistbinder is 50c each so a 4 drop worth.

A must have is card drawing because spamming out your creatures empties your hand but we're proud to present another Merfolk that could fit into that slot; Silvergill Adept. It was reprinted in Ixalan is cheap and provides a good body and card advantage. It's price is arround 10c each so a no-brainer.

Merrow Reejerey is our last good booster card we have. He is with CMC 3 the most expensive lord we have and but with it's ability and a cost of round about 2$ a very good extension. I used one or two on the field very often to spam my entire hand onto the board while untapping mana each time I played a Merfolk card or simply tapping opponents blockers for the final hit.

Last but not least Kopala, Warden of Waves. She is your best bet to negate effects from your opponent targeting your Merfolk that saves you another 4 slots of counter cards for a price of not even 50c each.

3 Cursecatcher == 1$ each == 3$
4 Master of the Pearl Trident == 5$ each == 20$
4 Lord of Atlantis == 5$ each == 20$
4 Merfolk Mistbinder == 50c each == 2$
4 Silvergill Adept == 10c each == 40c
4 Merrow Reejerey == 2$ each == 8$
3 Kopala, Warden of Waves == 50c each == 1.50$

Now we arrived at the supporter cards. I like your idea of using Simic Charm to protect your creatures in case something will break through Kopala's walls and to set the final strike to your opponent.

What makes Merfolk so strong playing, it is not the boost but the fact that our Lords will make creatures unblockable as long as there is an Island in play. To achive this, one usually plays Spreading Seas but it gots very expensive in my thought; 3$ each and so is near as expensive as our Lords. The cheaper alternative is Sea's Claim, from 8 Edition for round about 10c each it works as same as Spreading Seas but without the extra card draw so it might be a dead card in cases when opponent's play just Islands and nothing else.

Last but not least some kind of counter would be nice. As we play for budget, there is no chance to go for Remand as it is too expensive. Instead you might consider playing a 3 drop Unsubstantiate. It acts same as Remand without the card advantage but can additionally return a creature card to it's owner's hand. for a price of 10c each.

Something that could be considered as Vial replacement in this color combination is Nissa, Steward of Elements and her 0 ability. She is also able to predict our next draw with her +2 ability and can potentially win the game by her own. A big pro is also the mana gain if there is a land on top of the deck but ranges with round about 4$ near the Lords so consider not playing much copies.

3 Simic Charm == 15c each ==45c
4 Sea's Claim == 10c each == 40c
3 Unsubstantiate == 10c each == 30c
3 Nissa, Steward of Elements == 4$ each == 12$

There is a lot more to say to Modern Budget Merfolk and I already wrote 2 Primer Posts a while ago
https://www.mtgvault.com/risendeep/decks/merfolk-bdg/
https://www.mtgvault.com/risendeep/decks/merfolk-bdg-2/
so you might also look at these.

A last tip I have for your mana base is to play 3 drop Unclaimed Territory along with Hinterland Harbor really fits the mana base

5 mana sorcery type plainswalker against 3 mana + X instant spell; I know which one I would use ...

Details my friend, details XD

Whir of Invention turned out to be the best instant Artifact Tutor we have for these. I played over 100 matches with any combination of those Stax decks in modern format. With Lotus Bloom on Turn 3 and some artifacts played before, you have your whole deck open for choice

Just a version I fiddle arround inspired by your deck and my newest stax trys
https://www.mtgvault.com/risendeep/decks/protostorm/

Could be more efficient with some kind of early mana ramp like Mox's and Whir of Invention with several low cost artifacts to help Improvise ability. This way you also only need one or two Prototype Portal and have space for other cards.Problem with your Hailfire combo is that it lasts a turn so you should focus on instant effects or a Tezzeret plainswalker to finish the game

Very unreliable deck but suprising efficient if all combo pieces are in your hand. I tested it also with some extra mana gain from Chancellor of the Tangle and Time of Need to search the deck for Griselbrand so all you need is Goryo's Vengeance in hand. Some cards played in Dredge decks like Conflagrate or Cataric Reunion help getting the deck more stable and Pact of Negation to get your combo out for sure so give it a tr and a like

From the announcements:

"While a card seeing lots of competitive play doesn't by itself necessitate action, in this case we also see a reduction in diversity in the environment, an inability for the metagame to adjust, and a dominant strategy that's particularly hostile to rogue decks and innovation. For these reasons, Deathrite Shaman is banned in Legacy."

Just to now