To use OBS to capture the top-out window in combination with sound from ableton might be the best strategy if you want to get the most performance out of your system and only have one machine.
The issue, is that ableton is not the “slimest” program itself and will claim a certain percentage of your availabe processing power, mainly from the CPU. (only certain VSTs use GPU afaik, but its rather rare.)
Depending on the amount of tracks, sample rate, VSTs, etc. this will build up.
OBS is also using a certain amount of your performance. Here it depends on the encoder you use, whether it will consume CPU or GPU.
I would recommend to use the performance monitor in TD to optimize your patch, in combination with your system task manager. run your setup and watch what processes use how much of your CPU/GPU/RAM.
i would argue that the better idea is to have independent machines for TD and Ableton;
synch can be done with midi or osc.
If you want to avoid using OBS you can use external hardware recorders, like atomos or blackmagic devices f.e. These usually have HDMI inputs for video(+audio) and XLR connectors for stereo audio.
hope that helps.