on days of unstable atomospheric barometric pressure the elevation reading on the apple watch can lead to inaccurate results.
if all you want to do is get a pinpoint elevation for a certain place, it maybe off by up to around 20 meters or so.
apple is not promising anything better than that degree of accuracy.
if you look at the Compass app on the watch, there is a pane that gives your current elevation. and just below that there is a notation that the elevation given is good within +/- 20 meters.
having said that, in my case, my Series 8/WatchOS 10.1 does report accurate elevation consistently.
the discussion below doesn't fit exactly what you are looking for, but somewhat related.
if you want more accurate change in elevation info (for like when your running and want to track elevation change data), then i would do the following.
1. on iPhone: Settings/Security & Privacy/Location Services/System Services/ (then toggle) the setting Motion Calibration and Distance.
2. Go to the iPhone app Health. Find the Flight Climbed data page. Make the Watch your top level data source.
2. Go outside wearing your watch, with your iPhone in your pocket (near waist).
although the above is more purposely for distance re-calibration between iPhone and Watch, (the Support articles say you need to walk only 20 minutes on a clear day for this purpose), i have found that the above will be able to help with re-calibration of elevation as well, if you do as above, and walk up a hilly area, with a climb equivalent to maybe 20 flights (60 m).
doing this over a number of days made my watch and iPhone read the same altitude change and this made it correct (meaning fairly close to what the maps indicate as elevation change).
before doing the above, my watch would always underreport elevation change (compared with my iPhone).
after doing the above, it began to report accurately (but it took around 10 days before i could go out with only the watch (not along with the iPhone), before it consistently reported accurately.
you might also check the iPhone Health app to see what Flights Climbed data is actually being reported. i found that the data from the watch was actually being reported in the Health (interpreted in the Health app) correctly (!), but the elevation change number showing on the Watch itself was wrong, until i did the above re-calibration. you'll find data under Flights Climbed.
in the Health app you can actually re-order the list of devices where Health app gets its data from.