I haven’t done any research, but certainly there have been Grandmaster games that were identical to previous ones. (Sorry, I hesitate to give a %.)
Mainly this is because both players are satisfied with a draw, but very rarely a Grandmaster will repeat a previous blunder and soon resign. (No doubt this happens far less since computer databases became available.)
The length of time before a new move is played will vary by opening.
For example, the Ruy Lopez (1. e4 e5 2. Nf3 Nc6 3. Bb5) has been heavily analysed and it wouldn’t surprise me to see the same 20 moves being played - before the game really starts.
An off-beat opening like the Monkey’s Bum (1. e4 g6 2. Bc4 Bg7 3. Qf3 e6 4. d4) could easily see a new position by move 10.