As I work through my issues I'll edit this ...
1. Opening files (in my case, a .gpx file) cant be done as the app I use doesn't show in the share sheet, despite it using that app's icon as an icon for the file. The share sheet littered with crap like "open in notes" "copy to notes" "notes" (and the same three options for Dropbox) but doesn't actually list any of the navigaton/tracking apps I use that in iOS12 would be valid as an "open in" or "send to" option for the file.
2. Mail notifications (just the one test so far) are very messed up. Second email came in, and it worked perfectly. After getting up this morning and turning my phone on, nope, Mail notifications are still a total mess. For those interested, this is what happened this morning and yesterday ...
So, turned phone on this morning and unlocked it so it connects to WiFi. After a couple of minutes, the screen lit up (NO SOUND despite having it enabled) and new mail notifications came in. Screen went dark. I pick up the phone and the notification screen is EMPTY. Nothing. Unlock the phone and see that I've got a bunch of new emails as the badge icon is working. Swipe down notification centre. Still nothing. This is also what happened yesterday. In other words, email notifications come in silently and only show for a brief period in the notification centre before disappearing. I'm guessing, therefore, that 13.0 is similarly messed up and they're going to release it in that state. Hopefully to thousands of complaints.
3. FaceTime Audio calls continually drop WiFi and revert to 4G. This kills the call for about 10 seconds each time, and it happens roughly once a minute or so. Video calls, oddly, don't seem affected.
So, for me, my three main bugs haven't been fixed. And iOS13 has been in beta for many weeks now.