By "legacy" do you mean using an old version of the game? Just to be clear because I'd be down to try full game but I want to know how many worlds that would be
Edit: also don't currently know how to access old versions

for IL lag give better times, for full game lag is bad

You don't.

That being said, the rules state that time starts on the first frame of selecting the level, and ends on the first frame of touching the last trophy. You can just use one of the many video retimers out there.

Edit: oh yeah that's right, game rules exist. Probably should be fixed so that they match the category rules. I'm curious if this discrepancy affects any positions on the leaderboard

If you are looking for challenge you could try low% in some levels, you can't collect coins, gems neither kill enemies.
It was a full game category, but too hard to complete because trophies with coins above need a glitch to avoid like seem in this thread https://www.speedrun.com/tts/thread/3db5x
The moderators deleted the category, because there was nobody running it, but if the interest sparkle we could add it back.

Another ideas:

Pacifist%: don't kill any monster.
Kill%: kill every monster.
OneJumping%: don't use double jumping, idk if it's possible, if not then do a MinimalDoubleJumping.
MinimalJumping%: beat the game using the minimal amount of jumping possible, idk what the number is.
MinimalLeftPress%: beat the game using the minimal amount of pressing the left possible.
Damageless: beat the game without getting hit.
Death%: find the fastest way to die in the game. (Either a level or full game)

The ones below are more like Challenges than categories:

1Handed: it's more a challenge than a run, but beat the game using only 1 hand.
NoHands: don't use hands.
2Players1Phone: 2 players playing the game in the same phone, but one control the jumping while other control the movement.
UpsideDown: lock the screen and play the game with the phone upside down.
BackToHome: beat the game in the opposite order (level 40, level 39... level 2, level 1), so our hero can finally go back home.
AlwaysRight: beat the game while always pressing right (idk if possible)
Slowrun: try to beat the game as slow as possible, this may take hours.

The first frame was missing, you have to record the moment you press the first level because we use this was the start point to timing, you can't reset the first level

Same. I wouldn't mind having an extra variable or even an extra category since some might see it as unfair, but I'm not a mod so whatever works

The game is very unoptimized, it can give different times dependent on what device you are using and how many time the app are open. For me the game becomes almost unplayable after 30 to 40 minutes opened.

The whole point of speedrunning is to get the best time possible, so I suggest you go for it