My progress in a browser itch.io game got glitched,  which has me in a situation where attempting to start the game causes the game to freeze every time. Since it is, again, a browser game, I can't do the delete/redownload thing that's usually recommended. Also, there's no in-game button or whatever to reset my progress. How do?

Try clearing your cookies for itch.io, or if that fails, local storage. Beware that the former will log you out, and the latter will clear any data you have saved in other apps.

On Chrome you can clear individually what sites use as storage including cookies for subpages on itch, like game.itch.io,   and delete that if necessary. Ifit is embedded browser game, storage might not be itch.

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If you can't find it, make new naked profile and only go to game and look what is new in the  saved data hidden somewhere in the cookie preferences. At least for Chrome.