It sounds like your registrar reset your name severs on your way out the door.
You can check your current name servers with:
$ dig ns exmple.com +short
As you moved the domain to Cloudflare, the results you get back should be the names shown on the dns tab of your Cloudflare dashboard. If they are not, that is an issue.
$ whois example.com
If the name servers do not point to Cloudflare and the registrar on the whois is shown at Cloudflare, that means ionos changed them when you left.
Cloudflare support can fix this, to contact Cloudflare Customer Support, login & go to https://dash.cloudflare.com/?account=support and select get more help.
Please share the results from above and if you contact support, please share the ticket number and I’ll make sure it’s in the proper queue.