I use the dongle together with the Microsoft Modern Keyboard with Fingerprint & the Microsoft Surface Precision Mouse. Works perfectly under Windows 10. I don't know how far this can be transferred to two PS4 controllers, but I think it should also work.
That would be new to me.
The Ps4 only connects to selected Bluetooth connections of "Ps4 Gamer mega Bass 7.1 xx" - exclusive contract headsets/headphones. (Which are of inferior quality.)
Since the keyboard supports Bluetooth with multiple frequencies, I would think that would work. I have been able to connect all Bluetooth devices via the dongle. If you have the opportunity, try connecting the keyboard to a notebook that has Bluetooth. If that works, then it will also work with the Asus.
Unfortunately, I cannot answer your question.
But I can give you my assessment: I have had many bad experiences with Bluetooth (printer, camera) as well as good ones, so I regard this connection method as a game of chance. It may work well, but it may also not work despite a lot of effort. It's probably not the Bluetooth, but the software. The only thing that helps is to try it out.
Under Windows 10, a connection with the Airpods should actually work without any problems.
Regarding use under Ubuntu:
Unfortunately, we cannot answer this question, as we have not been able to test this in such a form. However, I will post your question in the community, and perhaps a user/other customer can help you further.
I connect my Sony headphones to the computer with the adapter, but it doesn't always work right away and I have to stretch everything out and reconfigure it. It also takes a surprisingly long time to establish the connection. However, the desktop is already old and has no BT function itself, so I can't say whether the additional devices are the problem.
Because many PC games only support X-Box controllers, search Google for DS4Windows.exe and it will work. This programme makes the PC think that your PS4 controller is an X-Box controller.
I connected my keyboard via this adapter and played games accordingly. Personally, I didn't find any difference between the cable and this adapter. But I only play games for fun/hobby without ranking etc. and am not dependent on the thousandth of a second. I hope this helps.
The Bluetooth adapter works without problems with Windows 10. Since the headphones have Bluetooth, this should not be a problem. I also connected my Bluetooth headphones (Logitech UE 9000) to my PC via this adapter.
With this device providing all the bluetooth functionality, I would say yes. If your camera doesn't have any proprietary quirks with the standard, that should play.