I haven't done this, but i imagine if you put your Ring Alarm Pro in bridging mode it should work correctly. Probably would not want to do the double NAT mode, as Starlink uses CGNAT and this would actually be triple nat as Starlink doesn't provide public IPs to end users. But it should work fine.

I have done this with the latest Starlink version. My Starlink hardware was new in September 2022. My Ring Alarm Pro base station was new in May of 2022. Everything worked well using the Ring Alarm Pro base station along with four eero 6 extenders throughout my home.... Until about a month and a half ago. Sometime in early December the Ring app quit recording motion alerts (or any events for that matter). I tried resetting the router, resetting Starlink, even full factory reset of Starlink and the Ring app would function normally for a short period of time but it would always go back to not recording any events. I still had our old 5G broadband internet running at the house, so I hooked it back up to the Ring base station, reset everything and it has now been working with no issues for about a week. I assume something changed with Starlink (at least in my area, Parker, CO) around the beginning of December 2022 that I haven't been able to resolve.