I believe the "Battery health degraded" or "Service" message will show once the battery hits 79%. Apple usually won't replace the battery until it goes below 80%. (The screenshot in the link below also shows 79% where this is mentioned.)
Once the phone experiences an unexpected shutdown due to the battery, it
should start throttling and state this under the Peak Performance Capability section. It'll also give you the option to disable the performance management, which would increase your chances of another unexpected shutdown again. This is not showing up for you, so the phone should be running at normal performance and the random shutdowns could be due to something else.
FWIW, the battery health on my spare XS that I use for browsing/games is 74%. I haven't experienced any throttling or random shutdowns yet, and it says it's currently supporting peak performance.
All of this is explained here:
Understand iPhone performance and its relation to your battery.
support.apple.com