It's not uncommon that the curl | sh method actually, among other things, detect what distro you're running and add the repos before installing via the package manager, so in the end it depends on what the script actually does. Atuin does it well for example: https://docs.atuin.sh/guide/installation/ -- and offers other options (as you should).

We're actually not going to be doing that for much longer. Lots of users kept querying how it was installed, where, how to remove it, etc.

The response of "it depends, we probably used your system package manager" was not often well received. Users who know how to use their package manager tended to just do that anyway, and not use the script.

I don't really understand the decision to completely stop doing it. If the script has logic to do A,B,C in different cases, why not just implement an --uninstall flag that does the opposite of A,B,C? Then users don't need to know or care what "type" of installation was done.

Of the three distros I know to more detailed extents, Debian, Arch and RedHat, none of those make it easy to install and keep updated a third-party package through the built-in package manager.

In all cases, signatures and repositories need to be configured, often requiring both root access and usage of the CLI and in all cases much harder than running an installer script (which might be doing exactly these steps).

To achieve easy means of installing using distro package managers means including the application in the distro itself, but now it's beholden to the distro's software update policies and thus stuck on that specific version for years or even decades.

That is not what a v0.something of an end-user centric desktop application wants for themselves.