My model so far has been to release the censored version of my game for free, and the explicit version for $2 while in alpha.
But when it moves into its first full release, I plan to increase the price to around $4-5.
I thought that it made sense that if people buy the game at an "early-adopter" price, that's a reward for supporting its development, and I'd like them to still have access to all subsequent updates / releases (on the same page).
But I foolishly forgot to check if that's actually the case; If they purchase it now, will they still keep access to it even after I raise the price later?

Provided they bought it (ie, paid money on it), it shouldn’t matter whether you change the price. Well, unless the files are delivered as “individually priced files” (ie, specific files being priced differently than the whole project).

Anyways, that’s the way I understand it.

The people who bought your game already own it and have the right to download updates (for the same project) even if you increase the price.

What you can't do is when you have a price per file (not the project, but rather a fixed price for a file within the project). In that case, it doesn't work because the price per file doesn't matter whether the person bought the project or not, but rather the price they paid.

https://itch.io/docs/creators/pricing#pricing-options

As you said. If you increase minimum price, this is early adopter discount. But better read the faq, if you plan on anything complicated like file prices.

Yup, won't be messing with "set a different price for this file" or anything - I mean just the project price.
Thanks for confirming!