If you buy and old domain name for your new website, it might be that Google uses the indexing settings of the old site with your new site until your new website has been checked. That’s what Google’s John Mueller said on Twitter:
We basically keep a list of the domains that we feel aren't ready yet. If you launch a new site on an existing domain, it doesn't automatically change the status of the domain — we'll still check to see if the domain overall is ready before removing it from that list.
— ? John ? (@JohnMu) August 18, 2020
Check your mobile rankings
The ranking monitor in SEOprofiler enables you to check the rankings of your web pages in Google’s mobile search results: