If a counter-offer (or the reason you interviewed with other companies) is about money, accepting it is IMO a bad idea -- the company wants to minimize the pain

If a counter-offer (or the reason you interviewed with other companies) is about money, accepting it is IMO a bad idea -- the company wants to minimize the pain of your leaving now, not the pain of your leaving in general. If you want to change what you do (coding to management, UI to AI, etc.) and the management offers you good options to consider, this is likely to be a genuine desire to keep you working for a company in whatever capacity. In this case accepting it should not put you on a path to the door.