@Stephan Bren
It will not automatically convert the users in the content database from classic to claims when attaching a content database from classic web application to claims-enabled web application.
So you could migrate the valid users from classic to claims-enabled by the command below.
$wa = Get-SPWebApplication http://webAppUrl
$wa.MigrateUsers($true)
And some site collection administrators deleted from Active Directory also will not be converted automatically.
So you could identify the site collection administrators by the command below, then delete them from site collection.
$web = Get-SPWeb http://webAppUrl/sites/rootWebUrl;
$web.SiteAdministrators
For more detailed information, you could refer to the article below.
Test-SPContentDatabase Classic to Claims Conversion
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