Gearset can retrieve and compare anything that the Salesforce metadata API can return to the application. If the metadata API cannot retrieve something, Gearset cannot render it. Standard tabs from orgs fall under this category.
When you try to retrieve a standard tab via Workbench, which also uses the metadata API, with the manifest file:
The result confirms that the metadata API does not support the retrieval of a standard tab.
Custom tabs created by users do not have this restriction.
As this is a problem with the metadata API, this behavior isn't a problem for git sources and targets.
If the metadata API is updated to support the retrieval of standard tabs in the future, Gearset would be able to too.
Standard tab visibilities
We have done some work to make it possible to fetch the visibilities of standard tab, that should not be a problem from August 2020 on wards.