Droid-ify can auto update apps in the background with root. I'm running it on GrapheneOS without root and it's doing it just fine.
It doesn't help with xposed but shizuku will accomplish a lot.
Indeed, rooting usually beats the purpose.
Not because it inherently makes you less private, but because having bad security makes it hard to be private, and opening up a way in android to allow apps to do what they want (selective root access) usually requires punching a lot of holes.
Even with AVBRoot, which allows you to setup Magisk or KernelSU with full Verified Boot support, you're still leaving open the possibility that something abuses the fact you're rooted against you.
But just so you know, if you insist, you can skip the step of locking your pixel's bootloader and install Magisk, but do not expect any support from that point onwards.
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