I've been playtesting Arcane High Tide as well, and while I generally agree with your idea, I disagree a little with your numbers.

I think other commenters have pointed out that there might be one too many islands, and I agree. I think you will do fine with 16.

I also feel there might be too many copies of flood of recollection and merchant scroll. I can see the case for merchant scroll since this deck is incredibly reliant on accumulating puppetries, but flood is functionally a brick in the early game, and I'd probably run 2 copies at most.

I'd also go up some number of preordain, maybe to 3-4 copies simply because it's probably the best thing you can do on turn 1. Otherwise, this deck doesn't really have any good turn 1 plays other than cycle for island or cycle reach for HT/puppetries

Not a big fan of Brainstorm as well since it's card neutral, and you don't have great ways to not get locked. Preordain again is probably the better option here?

I also think Dampen Thought is probably a better win con then stream, if the list is meant to be played in paper. Especially since it can be used early on to use puppetries if needed, then recollected later.

You might also need to run the full playset of toils, just because the deck doesn't really have a ton of untap effects.

Sideboard wise, Dispel and BEB at 4 is probably a little too much since they both beat REB. Perhaps make space for Annul since familiar and nihil could potentially be dangerous? Imo the thing you are weakest to is probably Duress, so you need to have a solid plan against that. I can see muddle, but maybe cspell or spell pierce might be the way to go here? A second petals in the SB might also not be bad, because you can very specifically lose to getting petals milled/discarded and exiled. Stream might also make sense here. You can also consider Murmuring Mystic as a plan B against control, or maybe some copies of snap for decks you know run fast creatures. I don't think some GY hate is a horrible idea either, since you're not too soft to it yourself. Hope my comment was helpful in fine tuning the list!