Can you send BTC from a Native Segwit address to a Segwit address?
Yes. Segwit (or rather Nested Segwit) addresses are actually P2SH addresses with a witness script. They should be compatible with most, if not all wallets since it was introduced fairly long ago.
The compatibility of whichever addresses that you're sending to lies purely with whether your client thinks if the address type is valid. Bech32 is valid for those services/clients who have upgraded to recognise it. Otherwise, in a modern wallet, you should be able to send within all the address types.