I'm pretty happy with Phoenix and I would label it as non-custodial. You've 12 mnemonic recovery words for your wallet. Taproot on-chain addresses are default.
As I currently don't have any payment channel open (due to only a small amount of Sats sitting in my Phoenix wallet after legacy wallet migration), I can't say much to unilateral channel control from your own side. Channel control should be covered by their documentation and FAQ section which isn't bad at all.
You've optional automatic channel creation for incoming payments (if your current incoming liquidity can't handle it, another channel is automatically opened for you; you can set a limit for channel creation fees which is very good if state of mempool is crazy; should automatic channel creation exceed your set limit, an incoming payment causing a new channel created would be rejected).
When you fund a channel Phoenix automatically gives you some amount of incomming liquidity (don't know exactly if it's some sort of percentage of your channel capacity). Nice feature so that incoming payments may not automatically need another automatic channel with its on-chain fees required (btw, Phoenix displays an estimate of current on-chain fees for channel creation, based on mempool waterlevels).
To enhance privacy, you can choose your preferred Electrum server for the wallet, even an own one. You can enable Tor.
To lock the wallet you can enable system screen-lock/unlock via fingerprint and/or a custom PIN code. Lock timeout can be individually set for the wallet.
My Android app version 2.3.9 currently shows BOLT12 payments "coming soon".
I don't have much experience with the app as I only used it as workaround app, but so far I like it. It's convenient, it claims to be open-source (frankly, I haven't checked, too small amounts involved so far), I like the amount of control and the optional automatic channel handling, also that you immediately have at least some amount of incoming payment liquidity.
I'm not a proponent of having a lot of value in a mobile wallet, regardless if on-chain or LN. My personal limits are in the ballpark of pocket money or what I comfortably would carry in my daily fiat wallet. YMMV...