I cannot help you unless it is a bug in the binding. The esp32 is a very low powered device and can have any number of firmwares loaded and I have no idea on what firmware you have loaded or what choices the firmware made. Because of the low powered CPU, the chip can not do high res and high frame rate video at the same time as regular snapshots. It has its limits and perhaps the firmware is making changes based on this. All I can suggest is you test the urls directly from the camera to see the results and compare, but when your getting snapshots the camera is not as capable for video, there is a trade off to be made.
I really think you should look at spending $10 more on a camera at least and you will get a far better result. The cheapest thing you can buy is not always the best VALUE you can buy. My esp32 cam just sits in the draw and only comes out when I need to run a test.
EDIT @maDDin1338
I did fix a bug last week that is merged that may have been the issue. But pausing and unpausing the camera or restarting openhab would reset things. If your using ffmpeg to create the stream and then edit the cameras settings to go back, it would not go back. The jar in this github PR will solve that or you can pause as a work around till the next milestone is released in a few weeks time.
Yes you can do that with the record to mp4 action. I use this to create mp4 files for each person that rings the doorbell that is timestamped. Then there is a MP4 history widget that makes displaying the recordings easy for the main UI. However you still have the issue with esp32 cameras that the stream is in mjpeg format and it takes a lot of CPU grunt to transcode it to h264. The widget could be modified easily to do the same with the GIF recording feature.
See the rule in this post for timestamps on the mp4 and gif recordings..
Custom Widget: Camera History and Live Popup - Apps & Services / HABPanel - openHAB Community
This post for the updated mainUI OH3 widget.
Camera MP4 Recording History and Live HLS - Add-on Marketplace / UI Widgets - openHAB Community
No idea, can you describe a way to reproduce this reliably? Suggest testing if the stream can be opened in a browser direct from the camera after pausing the thing.