First party or third party there is always trust. You don’t know that the “first party” custodians have your coins. You don’t know if their security model is any better than a cold card in someone’s basement. You don’t know the security budget allocated to that. A startup will not have the same level of budget allocated to security as a qualified custodian. We use a framework of qualified custody including on chain observability, state regulation, soc2 audited, etc. We assess the risks of the various models here: 
Ultimately, wire in and withdraw your bitcoin within 24h. During that 24h period they are in qualified custody with all of the above in place.
Swan Bitcoin
Assessing Risk in Bitcoin Custody
Swan encourages our clients to withdraw their Bitcoin to self-custody by offering free and automatic withdrawals.
