It does have the option to connect to your own node and the funds are non-custodial, meaning the application runs a full LND node and can create channels just like any other Lightning node.
Phoenix and Muun are also both non-custodial (I own my coins), but don't offer such low-level access where e.g. in Breez in case of an issue or something, you could literally go and manually force-close channels. Muun seems like a good option if you do a mix of Lightning and on-chain payments, since it keeps / moves part of the balance on-chain and another part off-chain. It should be practical for many users, however it often makes for more expensive Lightning payments (if the amount exceeds your 'internal LN balance', it has to be swapped on-chain with regular fees). A lot of time has passed since I last tried it though, so it's possible things have changed.