I had an issue come up today where a user wanted to search a SharePoint list by the default ID column.
The ID column cannot be indexed and is not searchable using just the ID number itself.
You can still search ID numbers in lists if you include the proper Keyword Query Language (KQL) syntax. Format your search as ListItemID:3 (replacing 3 with your own ID number, of course) and it will work.
And yes, this works in both modern and classic list search experiences and in SharePoint Server and SharePoint Online/O365.