LineageOS no longer comes with root installed, you have to install an extra zip file while flashing to enable it - https://download.lineageos.org/extras
IIRC some root detection mechanisms still check for an unlocked bootloader.
There's no root builtin, use Magisk with the Hide feature to prevent it from being detected by banking apps and such - even apps using the rather nasty SafetyNet work.
With that said, I highly question why any banking app would check root, mine doesn't and it seems to me like even if it did I could still use their website on my phone while rooted or my Windows machine with no sandboxing whatsoever. Requiring it just for the app seems pretty damn pointless.
A lot of banking apps store cached transaction data and authentication tokens on the "protected" (not accessable to non-root from other apps) part of the data partition. If you run without encryption or with either unlocked bootloader or TWRP installed, someone could just pull that from a device in recovery mode. That's also why unlocking the bootloader wipes your data partition usually.
This should be OR. If you have FDE enabled, then the data is encrypted and it doesn't matter if your bootloader is unlocked or you have a custom recovery installed -- all caveats about the trustworthiness of the crypto and strength of your key still apply.
IIRC some root detection mechanisms still check for an unlocked bootloader.