Are you trying to search for what bases a user has access to? Or are you searching for the user in a User field in record data?
There is no good way to search for a field value across multiple Airtable bases.
If you want to see what bases the user has access to, you need an enterprise account. The enterprise admin panel can show what bases and groups the person is in. With an enterprise account, you can also use the Web API to get more info about the user's access.
If you don't have an enterprise account, you can manually look for the user in the workspace settings for each workspace and see if they are a billable collaborator. However, that won't tell you exactly which bases have access, and it also won't tell you about read-only access.