I didn't touch that one for a few reasons, mostly addressed to exhaustion above, viz: mechanical timepieces tend to be based on a regulated entropic source (watchspring, weights). It's not clear to me that a slow resonance oscillator would effectively couple to gearing, and I'm very far from enough of a watch/clock nerd to think of how this might be done or whether there are any current or historical examples of same. Basically: if you had a pure resonator, then a mechanical coupling seems to me very likely to degrade its regularity beyond use in timekeeping. An escapement design is preferable, and again, that's an inherently analogue mechanism.

I can find no examples of an acoustically-based mechanical timekeeping mechanism. If you're aware of any I'd be interested in seeing them.

I can also remember when mechanical stopwatches were still A Thing, used in sport timing when I was a wee'un. I suspect that these were the highest-precision timepieces reasonably mass-produced (and likely expensive nonetheless), and they could reach 1/10th second accuracy. Far cheaper digital stopwatches came available shortly after, were less expensive, and had 1/100th s accuracy. They could easily have recorded to greater accuracy but the limits of human perception and reaction would have made that redundant.

Current prices seem to range from ~US25 to ~$150 for mechanical stopwatches, versus ~$2 to $20 for digital electronic stopwatches, going off Amazon.

Even now, timed events are generally only measured and judged to 1/100th of a second, given that unavoidable variances (e.g., in track or lane length for track or swimming events, or course lengths for others) would introduce variability not strictly addressed by an athlete's capability.