I'm using the Linux app, and whenever there's an update to Proton Mail, I need to visit the website, log in, download a package file, run it to execute the update, and then delete the file (or it just takes up space).

I'm not sure how it works in other operating systems, but all of those steps are annoying and unnecessary (and make it very likely that users won't install updates promptly). Proton mail is installed with apt (the standard Linux software-management program); it should update through apt as well, so updates happen as part of the regular process and don't require any of the slow, unnecessary steps above.