snapcraft VS mate-optimus

Back in the day, I used snapd, which is similar to Mac's Homebrew.

Hopping from one distro to another with a different package manager might require some time to adapt. Using a package manager that can be installed on most distro is one way to help you get to work faster. Flatpak is one of them; other alternative are Snap, Nix or Homebrew. Flatpak is a good starter, and if you have a bunch of free time, I suggest trying Nix.

My personal favourite IDE for java is Intellej Idea. Apart from not demanding the extra extension, It was designed special for Java and Java related languages so it runs java smoothly with great compilation time. so lets install it. Make sure you have snap before installing it

Linux Mints App Store is full of GUI programs, Snap Store ist full of it, Flathub is full of it.

You are being lazy. But I recommend bringing your ass directly to snapcraft.io and reading those documents in the Learn section!!

https://github.com/snapcore/snapcraft - not sure, but looks like a building tools for snaps

Besides, there may be other ways to install them, although there doesn't seem no such Flatpak packages in Flathub. For example, some senerio to use some release channel or Docker / Podman. Additionally, when you use a different Linux distro where systemd is adopted and therefore can do Snaps (Snapd), you have another possibility.

when I started out, I used red hat, Suse linux, and then finally I jumped to Ubuntu, when they killed gnome and rolled out their new GUI later, I switched to Ubuntu Mate, with xfce alternatively installed. And then later came MINT. which is based on ubuntu anyway.

Prepare a blank USB stick with a copy of Ubuntu (write the ISO to the USB stick with Rufus)

Ubuntu MATE (simple, well maintained, has the Ubuntu ecosystem support and should work well)

Linux Mint has its advantages, but your title doesn't make sense when there's Ubuntu MATE.

(btw: since the PC is older I would reccommend Ubuntu Mate or Xubuntu as those come with a lighter Desktop)

You can always change desktops later to Cinnamon or MATE or XFCE. If you want to try those desktops on your USB drive, you can download Ubuntu MATE or Xubuntu and try them on USB, just like you're currently doing.

My experience has been that Ubuntu's Gnome DE is somewhat less suitable to older computers than Ubuntu "official flavors" with lighter DE's -- Ubuntu Budgie (Budgie DE), Kubuntu (KDE Plasma DE), Ubuntu MATE (MATE DE), and Xubuntu (XFCE DE) -- all of which use somewhat less resources than the Gnome DE.

Consider looking at several of the Ubuntu official flavors -- Kubuntu (Plasma DE), Ubuntu Budgie (Budgie DE), Xubuntu (XFCE), Ubuntu MATE (MATE DE). I wouldn't bother with Lubuntu (LXQT DE) unless you need a lightweight distro, because the LXQT DE is not as mainstream or well-supported as the others.

Based on recent experience helping a handful of friends move from Windows to Linux, I suggest starting with an official Ubuntu flavor (Ubuntu Budgie, Kubuntu, Xbuntu, Ubuntu Mate) 22.04 LTS release, picking which ever desktop environment appeals to you. Official Ubuntu flavors are the Ubuntu OS layer with standard but different desktop environments.