Site Collection Administrator access denied when adding solutions

I have recently found myself in a situation, when after creation of a new, Modern Site (it was a modern Team Site) my account, even though that was set to be a SharePoint Administrator (even a tenant one :)) and a Site Collection Administrator wasn’t able to see links to any galleries in the Site Collection settings. Moreover, when accessing them using a direct links and then trying to ex. add a new solution, I was being told, that I have no permissions for that operation.