[Android Q&A, Help & Troubleshooting] V0latyle:
It depends on the device. There's the Android way, but then many OEMs insist on doing things their own way.

In both cases, you have to enable OEM Unlocking in Developer Options. This functions as a "safety" to allow the bootloader to be unlocked.

Here's where it gets tricky.

If the device follows the Android model, unlocking the bootloader is simple: in bootloader mode, you issue a command to the bootloader to unlock. This is usually fastboot flashing unlock. Some manufacturers use fastboot flashing unlock_critical or fastboot oem unlock while others use a token system and yet others use a third party software tool.

Samsung devices don't have a fastboot mode, and have some extra security measures in place, so they follow this procedure:

Now, the key. The "key" I'm talking about is the root certificate. If official OEM software is installed, the OEM certificate is also installed as the root of trust. If the bootloader is locked, it uses this certificate to verify the software on the device is authentic, genuine, and untampered. In this case the bootloader reports "GREEN" and no warning message is shown to the user.

A custom certificate can also be installed and used to verify custom/modified firmware. Examples of this are CalyxOS, GrapheneOS (both of which include a certificate that has been used to sign their software) and AVBroot (you can generate your own certificate and sign whatever you want with it). If a custom key is installed and matches the firmware on the device, the bootloader reports "YELLOW" state meaning a user installed root of trust has been set. This screen is shown during boot:

If the bootloader is unlocked, no checks are performed - you don't have to worry about the key, you can use whatever software you want because the bootloader won't check it. In this state, the bootloader reports ORANGE and shows this screen during boot:

Regardless of whether the OEM key or a custom key have been installed, if there is an error during verification checks (firmware doesn't match the key, for instance) the bootloader reports RED and displays this or a similar screen:

Now, how does this affect financial apps?

There are several different factors in play here:

The bootloader reports the verified boot state as "GREEN", "YELLOW", or "ORANGE". Apps are able to see this and know whether the bootloader is unlocked or a custom root of trust has been set.

Android natively supports Hardware Key Attestation which apps can use to determine that the operating environment is secure. If the bootloader is unlocked or a custom root of trust has been set, the chain of trust is broken.

Google Mobile Services is able to use these to detect whether the device is unlocked or the operating environment is modified, and can report this to apps via the Play Integrity API

Some apps also employ third party security engines which use various root detection methods instead of, or alongside, the native and Google attestation.

Thus, if an app detects an abnormal enviornment, it may have certain features disabled (like my bank's biometric authentication) or refuse to work entirely (like our other bank, whose app won't even work if Developer Options is enabled, even if the bootloader is locked on factory firmware)

I know this is a lot of information, so to help me enure I"m properly answering your questions, can you let me know if I've satisfied your curiosities, or if there is something specific you are wondering about?