Hi Teh,
Here are screenshots for your different situations from my test:
* classic interface (1)
Would your "classic interface" be below?

* power automate (2)

* Marketing App under Settings (3)
Would your "Marketing App under Settings" be below?

-> "It seem that the custom business process flow will not appear in the entity unless we are customize using the Settings within Marketing App and switch the process, then we can see the custom business process flow."
The reason can be actually found in your description.
All of those ways can be used to create custom business process flow, but if we do it with 1 and 2, we need to enable custom bpf to be available in marketing application,
(as you see in screenshot 3, my custom bpf which was created with 2 is not enabled and there are only 2 bpfs enabled by default, so I can't see it in marketing application if not enable.)
while creation and enablement are done at same time in 3.
Regards,
Clofly