LineageOS was great a few years ago when I used it with my older Nexus devices, but it doesn't seem as maintained nowadays. There's no images for the newer Pixel devices and no Android 10 support, which is a huge shame.
There's some speculation that the newer Pixel devices will be getting mainline (or close-enough-to-mainline) kernel support. So it should be relatively easy to work on a clean postmarketOS build for those, as opposed to relying on the AOSP-like LineageOS.
Lineage has never been very fast to release new Android versions. If Android 10 was out by now it would have been the fastest turnaround from AOSP release they've ever done.
Had a similar issue with GPS on LineageOS 16. Setting the GPS mode to 'Device only' fixed it for me. My guess is the other settings have a hidden dependency on Google Play Services, causing GPS to silently stop working if Play services isn't available.
I don't think people use ROMs as much as they used to. Especially since mobiles are so fast nowadays that they don't get slow even if the ROM is bloated.
Rooting with Magisk usually isn't enough to trigger SafetyNet failures (which is what most apps use to detect "rooting", among other things). I've been running rooted on my OnePlus 6 since day one without any app ever complaining, including google pay. Custom ROMs will fail SafetyNet typically, but there are ways around it if you want to keep hacking.
Magisk/stock is what I've been using of late.