Yeah, it is incovenient when you play Java and other people you know play Bedrock (or vice-versa). There is a community-made plugin called Geyser that allows Bedrock players to play on Java servers (it can be buggy sometimes but it is the closest we have to Java-Bedrock crossplay).

Bedrock makes it easier to play with friends, it also has cross-platform support (except for Linux and Mac). Console players can only play on featured servers (unless they use workarounds).

Java is better in most other aspects (I am biased for it though, since it’s what I play): you can mod it, play older versions, use custom shaders (with mods), no microtransactions, play on any server you want, (apparently) less game-breaking bugs, etc.

On console you can get texture packs and add-ons… from the marketplace.

On other bedrock platforms (Windows or Mobile) you can install textures and add-ons from your own files. The problem is that Bedrock add-ons are significantly less capable than Java’s mods.

binaries (executables) go in /usr/bin, flatpaks are installed in their own sandboxes, appimages are wherever you put them.

the shortcuts in application menus go in /usr/share/applications as .desktop files which link to the app, so the user generally won’t have to worry about where the executable is.

why would the app store ask you where to install stuff??

It’s called a graphical app store. Most distros meant for desktop usage that come with a desktop GUI have a software store. IIRC KDE’s Discover even has Flatpak support which leads to a higher variety of apps.

Otherwise, you can install an AppImage, or just a .deb file if you’re running something Debian-based.