The Person Who Wanted Your Job Is Waiting for You to Miss
You got the job. Someone else wanted it, and they hold the history and the relationships you need. They will not quit loudly. They will pull back a little at a time and wait for you to miss. Giving it time feels kind and reads as indifference. Lincoln showed the better move with William Seward: settle who decides in private, early, and then hand the rival real work everyone can see.