TLDR is at the end if you just want a quick summary.
There's quite a lot to sort through! I'll do my best here to answer your inquiries. I've responded to your thread so you're welcome to keep using this thread to poke me (or any other users) with questions. I hope it can even become a useful reference for others later on. :)
File type associations typically only become a thing if the user needs to double-click on that file type to open it inside the associated program. For text/image/HTML files this is useful to have but for itchio games I don't really feel it is necessary. If your save files are plain text files, why not just allow the user to open them in a text editor of their choice if they so choose? If you want to obfusticate the contents to mitigate cheating then that's up to you. For single-player games, I wouldn't really bother with any of that. Single player cheaters hurt nobody and want to enjoy the game in their own way. Let em do that :)
So for the question of file type associations, they are not necessary for your game unless you want to permit players to double click on the save file and open it automatically within the game itself. Not certain how yoru game functions so this may not even work even with file type associations. I'd recommend file type associations be an OPTION in the installer that the user selects and confirms instead of something automatically done. Many users don't care about file type associations and just want to play a game without registry edits (especially if they are a limited user and unable to approve any program that makes registry edits due to security settings). Itchio developer guidelines already suggest making games that do NOT require admin rights to install/play. They are good guidelines to follow.
The default Windows file dialog already permits specifying specific file extensions to look for. Just have the save files as a specific extension and then look for that extension when saving/loading the save game files. I'm not surprised with the Java mess as many people could see that crap coming from hundreds of kilometers away. The overwhelming success of the Android mobile market has effectively resurrected Java as a programming language in decently-high demand now.
If you package only for Windows then you're going to exclude entire portions of the market that can already play your game. Butler handles all of that without all the installer-specific bits. I'm not well-versed in Apple Products (neither iOS nor MacOS) because of how restrictive and closed the platform is on that end so I cannot offer any tips/advice in that regard. Maybe a Mac person can chime in and help things out :)
For Windows, I would do like many other programs and install to a more user-friendly directory like %USERPROFILE% or %LOCALAPPDATA%. The issue with %PROGRAMFILES% and %PROGRAMFILES(X86)% is how restrictive they are done by design due to how Microsoft did security for the OS. If installing in the user-friendly directories there are already default 'everything' permissions and no real need to fiddle with permissions or worry about write permissions for game updates and such.
TLDR:
Just use butler and get a nice cross-platform fully-supported platinum experience via itchio desktop application. Otherwise, you're going to want to change the default install directory to a user-friendly directory outside of %PROGRAMFILES% but let the end-user choose the directory & whether they want shortcuts & if they want file type associations to be done by the installer. Would love if the 'installer' was just an extraction & copying process like what the PortableApps 'installers' do for their various programs. No registry, no residuals. Just the files needed to run and function properly.
For other platforms it varies and it is far more in-depth than what I care to go into in this already-lengthy post. Linux-based operating systems that are Ubuntu & Ubuntu-derived (Linux Mint) typically use 'Launchpad' to add a custom game repository where the game is installed & updated automagically. The signup & approval & registration for this process is far too lengthy here. You're better off just using butler.