Been developing with Lazarus and free pascal for very long and been using linux for 27 years.
Gee, 27 years, honestly, I'd expect you to have mastered configuration by now.
1) The apt version is just downrightly an abomination. Fair, that is not only you fault, but also partly the distro packager.
Seems you understand the relationship with the distro packager, if so, why post about it here ? Debian have a great fault reporting process, everything gets looked at. I have mentioned that the way they, Debian, package, in distinct modules, causes user problems but they tell me it is what people want. If people like you told them of the problem it causes maybe they would reconsider ? Certainly nothing can be done from here.
2) Then installing directly from the Lazarus Website, you need to install three debs ....
Whatever I do after reading the "goREADME", installation of lazarus project clashed with the source.
e.g. "lazarus-project conflicts with lazarus-src ....
Yes, what you you expect ? The message, from the apt system, is quite plain, you are applying a Lazarus install when you already have a differently structured Lazarus install in place. Going to put a new engine in your car, remove the old one first !
Then trying to compile a KNOWN WORKING program, I get
... All sorts of errors because you are mixing two incompatible versions. You need to completely remove the repo based install, all its files and config data. It quite possible that apt may not be able to do that now you have cross installed, so look for any evidence of left over stuff. And remove $HOME/.lazarus too. And /etc/fpc.cfg and, possibly $HOME/.fpc.cfg
Then install your chosen model. I strongly suggest you install just FPC322 from the repo, use that to build the FPC324rc1 beta from source. Install that new FPC in user space, not root. Then build Lazarus 4.0 from source. Both builds done as you, the user and keep the results in user space (don't bother to 'install' lazarus, just run it from the built source directory). If you have been using Linux for 27 years, that should be a doddle. (remove, using apt, the FPC322 install when finished to avoid confusion). Set your $PATH to point to the new FPC. This is all doc'ed on the wiki.
If you cannot handle the above (and lots of people cannot), yes, use the official install debs from Source Forge. They will work OK if installed on a clean system, that is one with no residue of a previous, incompatible install. The one problem you might have is getting your fpc.cfg correct, FPC322 was not great, FPC324rc1 a heap better. But even with the old, FPC322 one, you, an experienced user, can edit it to what it should be easily.
Davo