A related bug MCPE-155740 was submitted a while back, but set to Resolved due to there being no steps to reproduce. The status comments said to comment or submit a new bug… I ended up doing both, as I don’t know if 2yr old Resolved bugs get reviewed:

Steps:

1. Launch minecraft
2. Click Play
3. Select a world from the Worlds menu list
4. After the world loads in, select Save & Quit from the drop down menu, which returns the user back to the menu screen.

Expected behavior:
The screen goes to sleep after the settings-specified amount of time of no user interaction. On my device, the auto-lock time is set to 2 minutes.

Observed behavior:
The screen stays on until the device drains of battery.

(Note:If you just stop at step #3, the screen will sleep, if no further interaction, as expected)