Gsync + HDR will both work at the same time regardless of what GPU you have, here's an old video showing just that with regular GSync + HDR: https://youtu.be/g0FMF97oKaM?t=865
'Gsync compatible' is 99% of the time a FreeSync monitor anyway, it just undergoes the extended testing to comply with GSync standards, 'GSync' and 'GSync Ultimate' have the dedicated processor in the monitor. Ultimate just adds a bit more testing and HDR 1000 certification.
Edit*
Worth keeping in mind that GSync Ultimate will go from 1Hz to the max refresh rate for the full VRR range giving the best experience. There is a good breakdown of LFC/VRR differences etc here: https://www.displayninja.com/g-sync-compatible-vs-native-g-sync/ - Even though the current GSync Ultimate module is a few years old now, it still offers the best experience.
Essentially it's a bit confusing, but for the absolute best experience, you want a monitor with FreeSync Premium Pro, or GSync Ultimate.
From my understanding, that should be impossible, i.e. Having Gsync and HDR running on a freesync (gsync compatible monitor). Took a few mins to google, found this....
How to Run G-Sync On A FreeSync Monitor
Here are our step-by-step instructions for using Nvidia G-Sync on an AMD FreeSync, G-Sync Compatible monitor, as well as what limitations you can expect.
www.tomshardware.com
Has it been changed since last year, i.e. made an improvement ?