Does rooting your device make you the root user or just gives you access to superuser utilities?

In linux systems the root user shouldn’t be used for daily use, you just make an user account with permission to use sudo, doas or su.

If you root your phone, at least with most tools, you don’t become the root user. Apps that use root access have to request it, and you’ll have to allow it in the root tool you flashed.

Example pop-up from SuperSU:

Lol. So if you use an exploit to gain SU what makes you think a malicious app can’t do the same? Or better yet, find a new exploit in the SU management software you installed. As soon as you root, you can no longer guarantee root activities are not taking place unbeknownst to you…

That goes for unrooted phones as well. The danger with rooting a phone comes from the automated software that is doing the initial rooting. It could install anything in there and the user would be none the wiser. Once it’s rooted and permissions are requested via the superuser app, it’s not any more dangerous than a non-rooted phone, assuming nothing malicious was installed during the rooting process, that is.

Once it’s rooted and permissions are requested via the superuser app

And you expect this piece of community software (that is often closed source to avoid detection by safetynet) is perfect? Never had any bugs or exploits?

it’s not any more dangerous than a non-rooted phone

The SU software itself is an attack vector. One with the ultimate payoff (root access). When you root the device you install a window in what was otherwise a solid wall. It is inherently less secure and I can’t understand how a knowledgeable person would argue otherwise.