No. See my discussion of this here. In .uk ,or .dz (Algeria), and other TLDs, some second level domain names are names, and some are labels under which domain names are assigned by the registrar (like co.uk). But if I wanted to register badger2022.uk then Nominet would show me dozens of registrars willing to host that as a second level domain. I could then host DNS servers for that and create foo.bar.badger2022.uk under it.
Trying to track the policy of hundreds of TLD registrars about name vs. label categories for their second level domains is never going to be elegant.