If you set the elevation at the start of rides, or have ‘saved locations’ with height data then I’ve found it to be pretty accurate.
If you don’t set the elevation start point then it should still accurately record height variation but absolute heights are likely to be inaccurate.
Strava elevation correct works but that means you have to log in to a PC which negates the usefulness of having a bluetooth connection to upload the data.
What does this mean? If you sync via phone and Garmin connect (to strava), does it not send the elevation data?
Having said all of that, elevation data is (IMO) a curiosity and not something that needs to be 100% accurate. It’s never going to be accurate enough to help navigation (although I have used it to show that we’re approaching a trig point in poor visibility) so it’s just about bragging rights to show how far you’ve ridden / how much climbing etc?