How to fix display position switching on Mac Studio

1) If one connection types (HDMI or USB-C to HDMI) is favoring main display after wake, then switch and use that connection for the Main display.

2) Possible unrelated, but it is also a good idea to turn Off all of the Spaces features in Mission Control when running a dual display setup.

Is one display often becoming Primary, and then the other, slow-to-be-seen display is aded as a secondary display later?

or can your Mac truly not tell them apart?

To determine display names and capabilities, you Mac uses something resembling "plug-and-play". it sends a query to the display, and the display responds with its name, its capabilities, including default and preferred resolutions, and its SERIAL NUMBER. The serial number is how the Mac uniquely tells TWIN displays apart.

<< The displays I have are TWIN displays (both the same make and model). >>

What we have seen here with TWIN displays, sometimes the manufacturers have been sloppy about what field contains the serial number. The Mac uses VESA standard, and if the display-maker does not supply the serial number in the expected field, the Mac can not tell the TWIN displays apart, and they 'swap around'.

Your displays have a design defect. only the display maker can fix this defect, and would have to issue a display firmware update to fix it. you should attempt to pressure them to fix the defect.

As a work around, two different model or different makers will not exhibit this symptom.

Another work around found by users is buying a little stunt box that intercepts the EDID information and lies about what display is connected:

https://www.amazon.com/s?k=edid+emulator+4k

additional background information:

the details can be seen using a Utility like SwichResX, which reads out the EDID information the Mac gets back from a query of the device for its name, capabilities, and serial number. in an earlier investigation a User found that the serial number was there, but NOT in the correct field, so the Mac could not tell TWIN displays apart.

Apple has not responded favorably to suggestions that they "accept whatever junk the display provides, whether it meets the accepted standard or not", but you can certainly ask again.