how accurate in feet and inches is the gps coordinates on apple watch ultra?

See the footnote at the bottom of:

Use the compass on iPhone - Apple Support

Important: The accuracy of the compass can be affected by magnetic or environmental interference; even the magnets in the iPhone EarPods can cause a deviation. Use the digital compass only for basic navigation assistance. Don’t rely on it to determine precise location, proximity, distance, or direction.

Gotcha.

First, the datum used by the county matters … a LOT.

If they used datum “A” and your mobile device uses datum “B” you might never find what you’re looking for.

To find the corner monuments, the watch might get you within range to find it … or it might not … or the metal monument just might not be there.

I can envision a frustrating day w/o closure if you can’t find the monument. (i.e. is it simply “not there” or did we “miss it”)

The tenting corners is a more interesting problem as you and your device determine the datum and you just need to return to the same general coordinates reliably enough to employ the metal detector.

Lat / Long are notoriously difficult to work with; I’d suggest an app that reads in Universal Transverse Mercator (UTM) or it’s simplified, easier to use cousin - US National Grid (USNG) coordinates.

There are quite a few iOS apps with this capability; not sure about WatchOS.

Without going too much into surveying theory and practice, do you already HAVE coordinates for the markers which you’re simply trying to find ?

https://www.gps.gov/systems/gps/performance/accuracy/

you could be off by 5 meters