Hows this oneThere is no reccording/streaming info in this log. Please run a local recording for about 20-30 seconds while playing, stop the recording, then upload current log file.
So do I do something with my game or with OBS because it’s not just minecraft that gets the laggy videos it also happens to other gamesEnable vsync or the frame rate limiter in Minecraft, you're overloading your hardware.
Enter Minecraft video op`tioins and enble VSync to limit FPS, as @Sapiens said.
You system is weak to encode live video. So, limiting FPS ingame helps you.
In any other game, do the same: search Vsync in video optionms and enable it lo limit FPS in game.
My system is fine here Its OBS that refuses to work correctlyIf your system is struggling to maintain a decent frame rate before OBS is even running then something else is going wrong here.
So what you suggest I do here (except get a new laptop)No it's not. You don't have a discrete GPU other than that Intel HD Graphics and that 'low-powered' i5 as it's only a dual core with hyper threading. That would be why you've got the U-type CPU on the 7200U.