I'm sorry, I don't follow you
If you are getting an audio and video feed via a HDMI capture card, OBS should not have an issue, if PC isn't overloaded, keeping those same source signals in sync.
But then, that isn't a video you'd play in another s/w player, but something you are capturing ... so I'm confused / missing something
Now, if you are talking about getting a HDMI feed from say a gaming console, then adding a separately routed audio signal ex. a microphone on the OBS PC... whole separate issue/discussion. And there are cheap HDMI capture devices that could cause their own havoc
this is a case of where the technical details matter.
Also, depending on OBS Audio filters/effects and their settings, etc, you could be causing an issue. For example, others have reported the RTX Noise reduction can have a significant CPU impact. There are plenty of Filters that could be applied (none by default) that could cause a problem. Or you could be doing something with audio at the OS level that OBS doesn't expect?
As for audio/video sync via the capture card:
- I ALWAYS recommend testing/troubleshooting audio and video signal inputs to OBS PC outside of OBS (OBS not even started).
- in your case, use Windows Recorder to record HDMI capture. Is that audio in sync. If not, OBS may be able to overcome the issue, but shouldn't have to, and I'd advise fixing the source/capture first, before moving onto configuring in OBS
the above are random thoughts due to not having enough info to go on
- PaiSand mentiond needing a recording/streaming session long enough to capture performance metrics, but you never posted an updated log
- and I'm confused by your posts, so a detailed description of the audio and video paths, and any outside OBS processing on those signals (as not captured in OBS log) would be needed to assist further