How do I lock the dock to a specific display on Mac Studio with 15.5 Sequoia?

The only way to lock the macOS Dock to a specific display is with the DockLock Lite app from the Mac App Store.

You select a screen, and the app makes the Dock stay in there no matter what.

Note: Most of us used to use the dock at the Bottom, and disabling Displays have separate spaces removes lots of macOS useful features, but with the app you can keep it on!

Yea' sadly they just keep adding one new features on top of others.

To keep my Dock in one place and the Desktop window panels from moving, hiding and resizing.

I use the following Stage Manager, Tiling and Mission Control settings on my Mac's with multiple displays.

👍🏽

When the Dock is placed at the bottom, it will appear on either display, when you bump your cursor against the bottom of that display.

There are two things you can do to change, or at least mitigate this, since you don't like it.

1) Place the Dock on one side instead of the bottom. This way, if you have two displays side by side and choose Left, the Dock will always stay on the left side of the leftmost display (similarly if you choose Right, of course).

2) Hide the Dock and add a meaningful delay to the autohide feature. This makes it harder to make the Dock appear if you accidentally bump against the bottom of the "wrong" display.

Also, you may onsider relying less on the Dock.

I for one do not use the Dock at all...

You're welcome.