How ever did you guess must be all my suggestions on the forum about using offline maps!
Yes, I am using Mapbox and my layer is a .mbtiles raster, generated from QGIS, based on Ordnance Survey Zoomstack data plus my own data (combined vector layers converted to raster as I've described elsewhere on the forum - View GPS point on Map for Blank Forms - #7 by seewhy).
I have just done another test, and fortunately I'm 150km from the .mbtiles map extent... So that means my basemap is not 'in range' when I use the same form at home, but with the Mapbox background mapping visible I can reproduce the issue that you have referenced for point markers, but in my case the location circle / cross is still visible when I shut off the screen and wake it again, so not all overlays are destroyed if there is no offline map layer visible on the screen - I didn't notice whether the point marker was also destroyed while I was on site, and I'm not going back for about 2 weeks so can't check that easily!
When I created my offline layer, I set the zoom levels for my .mbtiles layer to the range from 10 - 18 and I recollect that when zoomed out so that my layer was not visible there was a location cross, which disappeared as soon as I zoomed back in - I thought it might have been rendered below the .mbtiles layer so was hidden, but as I was trying to do fieldwork, I didn't test every scenario...
In my usual tinkering style, I saw that there was a bit of a workaround for the 'destroyed' point marker... I noticed that the new marker button and delete buttons were inactive when waking the screen, but if I long-tap on the map to create a new marker location (my appearance setting for the form allows me to!), then a new marker appears, and I can then delete it and reset it to the GPS location (for example) without closing the widget and starting again. Not sure if this is relevant to solving the issue, but may be of interest.
Thanks for your prompt help, appreciated as always.