How to correctly set the PATH variable

A lot of tools (like rustup) modify the PATH variable by adding some code to the ~/.profile file.
Usually the .profile file is sourced when logging in.

In clear linux ~/.profile is not sourced.

What’s the recommended way to edit the PATH variable?

It should read ~/.profile as far as I know. It should also read /etc/profile and /etc/profile.d/*
See this threads comments: Alias as root not working

It does read /etc/profile and /etc/profile.d because in the default ~/.bashrc there is

if [ -f /usr/share/defaults/etc/profile ]; then
	. /usr/share/defaults/etc/profile
# allow admin overrides
if [ -f /etc/profile ]; then
	. /etc/profile

But it doesn’t source ~/.profile anywhere. In other distros the file ~/.profile is sourced when logging in.
I know the file is not sourced when running gnome on wayland but in clear linux it’s not sourced even when running gnome on xorg.

According to the bash man page, bash is supposed to read it automatically, but I think it has depended on /etc/profile to do this - so, from a quick glance, this looks like a bug based on an incorrect statement in the bash man page. Worth fixing, of course.

It did source ~/.profile for me with an interactive SSH login, but not in a desktop environment as @ranfdev is suggesting.

The way I’m understanding the documentation, it sounds like this is the designed behavior since launching GNOME terminal is not a login-shell?:

Yes, It is the designed behavior of bash. But usually, desktop environments are launched from a login shell, so every terminal you open inside that session inherits all of the environment variables (even if the terminal is not launching a login-shell).
The gnome team has written about this, but here the situation is a bit different:
~/.profile is not sourced even on Gnome on xorg
I can’t get the workaround using environment.d to work (the path variable is still the same, even after adding a file with the correct config under ~/.config/environment.d/path.conf

At the moment i’ve set gnome terminal to launch a login-shell every time, so i can access my environment variables, but only from gnome terminal