I think you are a little confused at the problem here. The issue is that partial updates are not supported. The reason for this is very simple, Arch ensures that any given package list works on its own, but not that packages from different versions of the package list work together. So if Firefox depends on libssl the new Firefox package may depend on a new libssl function. If you install that version of Firefox without updating libssl it will cause problems.

There is no way around this limitation. If you install that new Firefox without he new libssl you will have problems. No matter how you try to rules lawyer it. Now 99% of the time this works. Typically packages don't depend on new library functions right away. But sometimes they do, and that is why as a rule this is unsupported. You are welcome to try it, but if it breaks don't complain to the devs, they never promised it would work. But this isn't some policy where you can find a loophole. It is a technical limitation. If you manage to find a loophole people aren't going to say "oh, that should work, let's fix it" it will break and you will be on your own to fix it.

Focusing on your commands. The thing is that pacman -S firefox is always fine on its own. If Firefox is already installed it will do nothing, if it isn't it will install the version from the current package list. Both of those operations are supported. Also pacman -Rs firefox && pacman -S firefox is really no different than just pacman -S firefox (other than potentially causing problems if the package can't be allowed to be removed due to dependencies). So your command isn't accomplishing anything even if it did somehow magically work around the rules.

What is really the problem is pacman -Sy. This command updates the package list without actually updating any packages. This will enter you system into a precarious state where any new package installed or updated (example our pacman -S firefox command form earlier) will be a version that is mismatched with the rest of your system. This is unsupported and will occasionally cause problems. Generally speaking you shouldn't run pacman -Sy, any time you are using -Sy you should also be passing -u. This ensures that the package list and your installed packages are updated together.

it's just unsupported. like, if something breaks by that happening then it's not a bug, but your fault.

installing a new package without updating is the same as updating a single package

I feel like there is an underlying issue here you're trying work around. Why do you not want to update everything together?

You're correct partial upgrades are unsupported. Arch follows a rolling release model, meaning there are no fixed "versions" of the system. Instead, everything is continuously updated. Each package is built and tested against the current state of the rest of the system in the Arch repositories. That package was compiled against the latest system libraries in the repos, not necessarily the ones on your machine.

Your proposed "workaround" may work if the package is standalone and has few/no dependencies. Again, ArchLinux strongly recommends full system upgrades (pacman -Syu) rather than only reinstalling/upgrading a single package, because library or dependency mismatches can occur if your system is out of sync.
A safer approach may be to use "pacman -S package --needed" which will avoid removing it first and automatically handles dependencies safely.

but installing a new single package if it wasn’t there is okay.

Not true. It says clearly "Partial upgrades are not supported". Whether the package was there or not is irrelevant. And I really don't mean this personally, but as general advice, using Archlinux and its wiki requires a modicum of independent thinking.

edit: clarification:

It is OK to use '-S' only if all installed packages are on the same level as the local package info. That is assuming that the cached local version of the package is still available on package servers.

Also read https://wiki.archlinux.org/title/System_maintenance#Partial_upgrades_are_unsupported

It is only a partial upgrade if you update your databases, without upgrading the rest of your system. If you try to pacman -S firefox, and it gives you a 404, you have to both update your pacman databases, and upgrade your packages. This will only give you a 404 if you cleaned your package cache, and your package is out of date. Usually, -S on an already installed package will reinstall it from cache. This does not cause a partial upgrade.

If you run pacman -Sy, everything you install is now considered a partial upgrade, and will break if you don't know exactly what you're doing. In order to avoid a partial upgrade, you should never update databases (-Sy) without upgrading packages (-Su). This is usually combined in pacman -Syu.

When installing on Arch (or a derivative) you should run sudo pacman -Syu package_name so it is always up to date.