1. Does the package Manager just run the most stable version of Libre office?

more or less, debian and by extension mint prioritize stability over the newest stuff, so the new versions are added later than bleeding edge distros after some of the quirks are ironed out, of course distro agnostic package managers like flatpak do not follow this rule so they tend to have the newest versions available

2. Is there a better way to update my programs using the package ? Even if it’s a terminal window command?

The software center is just the frontend for the terminal package managers so updating with either one will get you the same results. If you want something more up to date you can try installing with flatpak, or other package distribution ways like appimage. Either way in my experience unless you're running bleeding edge hardware or similar, there doesn't tend to be too much you're missing out on

I stick with the package manager for most things out of convenience, but I install the latest version of Blender, GIMP, and Jellyfin manually because I use them a lot and the feature upgrades can be significant.

If you're five, I'm six, so I can't help more than that.

the flatpak version is generally more up to date in my experience. but you can also sometimes go directly to a software's website and find their packages, which is also more up to date. Like Audacity for example has a new version out that isn't in the mimt manager yet.

Debian and Mint likes to use stablty over cutting edge software and the update app is just a frontend to apt even updating from terminal gives same packages