Kodi only accepts htsp
The client is HTSP so that''s probably why.
Nevertheless, pass is default and also used for recording.
I have never struggled with stream settings as defaults worked. Now I tried to enable the Restart on error: option and disable the Switch to another service: option for both htsp and pass profiles to see if there's any change when the signal level drops...
Possible bad (new) Haupagge tuner?
Well, try the USB 2.0 port as well... USB 3.0 is not always the best choice for some devices. Also, the dual tuner stick is a bit power hungry. There's no extra power reserve on USB ports of RPi 4B, it also depends on your power supply. So you may try to use some USB hub with external power (or make a USB cable fork to bring a hard 5V to your USB tuner).
My tuners sometimes hangs after switching to another channel but it's then visible in dmesg output and in this case USB port power off / on is necessary to make it working again (I suppose the reason is most likely the low power / long USB extension cord issue).