Let's say I have a wallet with a non-native segwit address (prefixed with 3- like multisig).
Can I send my utxos from this address to a native segwit (bech32) address?
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The wallet needs to be able to decode a bech32 address and construct the appropriate native witness output when sending funds.
Given that your (hypothetical) wallet can spend P2SH(witness) outputs already, it is likely it can or will soon support native bech32 addresses, but there is no guarantee that the latter must be supported given the first.