Serious bug in Microsoft Visio (Professional 2021)

Renumbering is working correctly for me in Visio Plan 2, which is essentially a superset of Visio Professional that you have. I'm not aware of any differences in the P&ID template between those two versions, but let me know what you see that's different from this:

I dropped three shapes:

deleted them and dropped two more

Then, on the PROCESS ENGINEERING tab I selected Renumber

and in the renumber dialog I made my choices and clicked OK. (note that you need to indicate which equipment type(s) should be renumbered)

with this result

I know that's what you were expecting but didn't happen. Do you see anything different on your Process Engineering tab or in the renumbering dialog?

Interesting. I can recreate your success in a simple file, but not in my more complicated file with custom tags. My conveyors, tagged "CV-x" don't number correctly. It seems CV-1 is always there, but then it starts from CV-6. Deleting CV-1 and adding a new conveyor results in it being tagged C-1. Deleting, say, CV-7, results in it being tagged the next largest number. Bizarre.

Alright, I have tried copy and pasting my design into a new sheet again, and this sparked a eureka moment: a pop-up prompts you to reference/hyperlink the pasted shapes to their source. Clicked "cancel" here and now renumbering is working correctly. Thrilled. Hope I haven't spoken too soon.

I'm glad you found a way to restore the renumbering! Keeping my fingers crossed that it continues to work.