

I’d recommend checking out Distrobox, which allows you to create containers of other Linux distros then export their applications as if they were native. Install a distrobox with one of the distros that this program works with, use the terminal to install the program within it, then if it isn’t immediately in your applications menu use the distrobox export feature to place it there.
You could also layer Nix onto your bazzite image and install it that way, but if you don’t know Nix it’ll be complicated
Professional audits happen for big projects, and hobbyists audit the programs they use frequently. In addition, some projects adhere to the reproducible builds guidelines, which ensures the packages you’re receiving are identical to the upstream repo. There’s more work to be done in formalizing and automating these processes but this isn’t a major issue by any means