Verify the records, not the symptom.
Migrations bring a specific worry: you changed a record at your DNS provider, and now you keep refreshing the site to see whether anything happened. Check the records themselves instead. Run DNS Lookup before touching anything to capture the current state, again right after saving your changes, and once more later to confirm caches have moved on.
The tool queries A, AAAA, CNAME, MX, TXT, NS, SOA, SRV and CAA in parallel, so you catch collateral damage early. Plenty of migrations break email because someone rebuilt the zone on a new provider and forgot the MX and TXT records. The Email authentication panel at the top shows whether SPF and DMARC are still published, and it warns when a domain has more than one SPF record, which makes SPF fail.
One thing to keep in mind: the lookup runs through the resolver you pick, Google by default, and any resolver can hold a cached answer until the record's TTL runs out. Switching the resolver list between Google, Cloudflare and Quad9 shows quickly whether they agree, and DNS Propagation Checker asks a dozen of them at once. To see the value straight from the source, query one of the domain's own nameservers, for example dig @ns1.example-dns.com www.example.com A.