A default installation of a Content Delivery (CD) instance uses only a Web database. However, some site definitions might refer to the Core database:
<site name="shell" .....database="core" .... <site name="login" .... database="core".... <site name="modules_shell" ..... database="core"
So, the above error message can be found in CD log records. Sitecore KB article [#KB0137194] (support.sitecore.com/kb?id=kb_article_view&..) is also available for reference.
To resolve the issue for error messages, you can follow the KB article but if you are using EXM then it will give an error for the shell site.
In that case, you should inherit EXM site with "website" to resolve the issue as:
<site name="exm"... inherits="website" ... />
This applies to Sitecore 9.1 (initial release or higher) and it is fixed in 10.0.0 (initial release).
Happy learning :)