Can pruned Bitcoin nodes be trusted to provide UTXOs for multisig vaults?

None of the actions you listed require more than a pruned node. Pruning only removes historical block data (the entire transaction) and does not change the included UTXO set (which is maintained separately).

in particular:

Returns all UTXOs for an address.

Simply, this can be done by: scantxoutset RPC does not require complete blockchain data. Note that (depending on your hardware) it may take several minutes for RPC to perform a complete set of UTXOs (pruned or not).

Alternatively, you can use Bitcoin Core’s built-in wallet to import addresses or their output descriptors into a monitoring-only wallet (which does not have a private key). This will cause the wallet to track all UTXOs (and also all transactions) that affect the balance, regardless of whether they are pruned or not.

Of course, you can also connect other wallet software you have to your node. Depending on what kind of software it is, it may or may not be affected by pruning.

Provide the script information and values ​​necessary to build the PSBT,

If you know the outputs used by a transaction, you can construct the transaction’s PSBT without accessing the UTXO set. However, you must enter this information before signing. this is, utxoupdatepsbt RPC (if not already done by the wallet software) (UTXO is usually already recognized anyway).

This is not affected by pruning.

Verify your spending;

This is the most basic functionality of Bitcoin Node software. Not affected by pruning.

And broadcast the transaction?

Not affected by pruning.