Definitely a head-scratcher. Do you use the GMail app on your phone? And if so, do you know if it runs in the background?
If it does, then seeing the emails disappear would suggest they’d literally just been lost/moved/deleted moments before.
Definitely worth checking the activity of your account to see if any unrecognised parties are accessing it.
This article says it should be possible:
https://support.google.com/answer/2452063?hl=en#:\~:text=We'll%20list%20the%20IP,bottom%20of%20any%20Gmail%20page.