Try this:
If you are using logitech webcam software/utility (should be in your system tray), open it and disable any of the features in this dialog (yours might look a little different, but should contain the same options, turn off Follow My Face, Right Sound and Right Light. Autofocus can even be turned off if you don't need it such as if the camera is focused fine where it's at and you're not going to be moving objects close and far away a lot to the lens. Also try adjusting gain manually if you have the option and disable the automatic gain. Basically anything with a check box turn it off, and adjust settings manually to get the right image. I'll explain the reasoning below... Sorry I don't have a logitech camera hooked up right now to show you exactly so pardon these web grabs.
Honestly when I do have my C920 hooked up, I don't use the logitech software at all. I don't install it. Because it's bloated, slow, and to me does more harm than any good. Also you can access all you need to to configure the camera using the webcam configuration dialog within OBS, Simply click right click on the webcam source, click properties and then hit Configure Video. From there you get this dialog:
This is from my current webcam. Notice how I don't allow it to AUTO anything, I've manually adjusted everything. That's because when you let the camera do all these functions, and if you have it set to do the "fancy features" like Rightlight etc. the camera has to do double duty to process these functions and algorithms to the point sometimes, many times, where framerate suffers in a big way. So I would suggest unless you really need the logitech software for the webcam
(not speaking of the drivers, of course those help but aren't actually necessary to make the camera function, you can always use the basic USB_VID driver for the camera) disable the software by closing it out of your system tray, right click it and close it, but before you do that make sure you've already gone into it and turned off all of the features.
Now see how your camera is doing in OBS. If the issue still persists, then go into the configuration of the camera in OBS as instructed above and check to make sure that nothing is checked there. You should be getting full frame rates at that point. Of course you may need to adjust the image so use this same dialog to adjust all that you need. Keep in mind I noticed your video was slightly dark, so adjust your exposure to a good level, and you should notice the camera go into full speed at that point.
If the problem persists, please post a log file from OBS, also if you can screen cap the above two "Properties" screens from your camera (again go to OBS, double click your camera, click on Configure Video) you can screen cap each window by clicking the window to ensure it is active then use ALT+PRTSCRN (Print Screen Key) to capture just that window, then you can Paste that directly into your response, do it for both the Video ProcAmp and Camera Control sections like above.
Let me know if this helps, pardon my lack of formatting and maybe incoherency as I've been up fixing code for like 12 hours still since yesterday lol, anyway if you still need more help let me know! We're here to help!
SPIKEYPUP / Patrick Ewalt
