Most packages managers can run arbitrary code on install or upgrade or removal. You are trusting the code you choose to run on your system no matter where you get it from. Remember the old bug in ubuntu that ran a rm -rf / usr/.. instead of rm -rf /usr/... and wiped a load of peoples systems?

Flatpacks, Apparmor and snaps are better in this reguard as they are somewhat more sandboxed and can restrict what the applications have access to.

But really if the install script is from the authors of the package then it should be just as trustworthy as the package. But generally I download and read the install scripts as there is no standard they are following and I don't want them touching random system files in ways I am not aware of or cannot undo easily. Sometimes they are just detecting the OS and picking relevant packages to install - maybe with some thrid party repos. Other times they mess with your home partition and do a bunch of stuff including messing with bashrc files to add things to your PATH which I don't like. I would never run a install script that is not from the author of the application though and be very wary of install scripts from a smaller package with fewer users.