We really need to move away from the idea that a user having control over his/her device is insecure.

I can use online banking and paypal with windows logged in as administrator or GNU/Linux logged in as root[0], why shouldn’t I be able to use google wallet pay wallet with root?

[0] yes I know you shouldn’t log in as root, but that doesn’t change that you can do it.

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…

if you use an exploit to gain SU what makes you think a malicious app can’t do the same

They can. 99% of computer security is still not installing malware or being tricked into taking actions that enable your own harm. That said often rooting methods involve physically pressing keys while booting to access the boot loader, ADB, running things with with expansive permissions. Malicious apps install via play store with reasonable permissions will generally have a much harder time breaking out of the sandbox.

Or better yet, find a new exploit in the SU management software you installed

Historically “sudo” tools haven’t been the source of many issues whereas a multitude of problems flowed from complex memory unsafe code.

As soon as you root, you can no longer guarantee root activities are not taking place unbeknownst to you

You can never guarantee this however if you are careful what you install you will remain safe same as it was before.