Hi guys, one more update from my end.. now I'm certain. The issue happens always from Sunday to Monday (CET). This morning again I was logged out. Memory or space is definitely not an issue. I'm certain I have closed all open apps in the evening before going to bed. I'm on iPhone 15Pro 256GB, plenty of space available.
From the 'error console' within the app, the only thing I can't run is the "Test native storage" - nothing happens when I click on the button if that helps.

info
{
"webViewVersion": "17.3",
"name": "iPhone",
"diskFree": 4460531712,
"diskTotal": 255866785792,
"manufacturer": "Apple",
"isVirtual": false,
"realDiskFree": 137513206334,
"osVersion": "17.3",
"iOSVersion": 170300,
"memUsed": 113688576,
"realDiskTotal": 255866785792,
"model": "iPhone16,1",
"platform": "ios",
"operatingSystem": "ios"
}