MTA-STS has more than one moving part.

DNS

Query _mta-sts.example.com and record the policy ID.

HTTPS

Fetch:

https://mta-sts.example.com/.well-known/mta-sts.txt

Confirm it is available over valid HTTPS and contains the expected mode, MX patterns and max age.

SMTP endpoints

Make sure the real MX hosts match the policy and present certificates acceptable under the MTA-STS validation model.

Reporting

If TLS-RPT is configured, use reports to identify which senders are seeing policy or certificate failures.

Reference material