AngWay I don't have all the answers, but I'll answer what I can.
AngWay Auto-update is enabled (WiFi + data), but apps don’t update — I still see pending updates days later. Is this normal or misconfigured?
This is not a GOS-specific issue. I'm the "IT support" for my extended family, and I run into this issue all the time. I've configured all of my relatives' stock Android phones to do auto-updates through the Play Store, but some just simply don't work no matter what I do. Everything is correctly configured, they never touch any settings, and yet the Play Store just won't do auto updates. Some of them even have identical phones & setups, yet only some of them get auto updates & others don't without any indicators as to why.
Not that knowing this helps with your problem, but at least it's not a config issue on your end. But just to make sure we're on the same page, grant the Google Services Framework unrestricted battery usage, background data usage (if acceptable), and the Internet permission, and grant the Play Store background data usage (if acceptable), app install permissions, and the Internet permission.
AngWay Every update requires a second confirmation tap. Any way to make installs fully automatic?
This is app dependent, from both sides; it depends on both the app you want to install & the app that iniates the install itself. Some apps can do silent updates (like Obtainium, the Play Store, and the Aurora Store), and some can't (installing updates through APK files & the File Picker always pops up the update window, for example). Some apps accept background updates just fine, but some always pop up the installation dialogue (I'm looking at you, PipePipe) no matter which app I use to update them (Obtainium in this case). I'm not sure what the criteria is for either side, unfortunately; I just know it's a thing.
AngWay If I uninstall Play Store after installing apps and switch to Aurora Store, will it break updates or cause issues with existing apps?
That depends on the app(s) in question. If some of your apps genuinely need Google Mobile Services (GMS) to run, then they might break. Many apps can run just fine without GMS being present & just claim to need GMS even though they don't; you'd have to test with each app individually what's their case.
Some (but not all) commercial closed-sourced apps will check their installation source & block their usage if they detect they've been installed from some other source than the Play Store. Do note that if you update an app through the Aurora Store, the app's installation source will be marked as Aurora, even if you originally installed it from the Play Store. Not that many apps do this check, but do note that it's a possibility.
Aurora Store itself can update apps just fine, even if they were originally installed from the Play Store. I haven't personally tried any background auto updates through Aurora myself, so I can't comment if they work or not. Manually checking & installing updates for apps originally installed from the Play Store works fine though.
Good luck.