I use a built-in screen recorder on my computer and when I review footage I notice that the livesplit timer I use wasn't present. should I use different recording software?

Yes, I would always recommend using OBS unless there is a very specific reason why it doesn't work.

Yeah I'd just recommend using OBS since it's not hard to use and it's very customisable but I will note that you don't need the timer on the video as the mods can retime the run but it's obviously preffered.

Built-in recorders and just recording software, in general, tends to grapple onto a running application to capture, sometimes from a specific engine, so it prioritises the application for recording and sets this stuff back