I will explain to you how it's implemented, but I don't believe it's what you want.
I have 4 monitors. When I set the dock to "bottom", with auto-hide off, moving to the center of any of the monitors cause the dock to jump to the bottom of that monitor and stay there until I do the same on another monitor.
If I set the dock to the left or right, it will remain permanently on either the left-most or right-most monitor.
I do not believe it is possible to have the dock on the bottom of ONLY one of the monitors. It just doesn't work that way.
Unfortunately, sometimes the answer is "You can't do that."
There may be a third-party app somewhere that would allow you to pin the dock to the bottom of only one display, but I'm unaware of any.
My suggestion is that you file a RADAR with Apple and request it as a future feature.
I can envision writing an app that would do what you're asking, but given that a quick check of all the multi-monitor software developers and video editors I know shows all of them with either a left-side or right-side dock, the audience would be insignificant...if I thought I could get 200 people to pay $1, I'd set up a Patreon and do it, but I think you're a lonely unicorn...
See Why does my dock keep moving back to my other monitor?