Do I need a HDMI Switch or Splitter and what do I need to look out for?

So to summarize quickly here's the plan/general target I'm working towards...

I'm currently living with my brother at the moment and we share a TV but here soon I'm planning to buy a PC as well as all the accessories including a Monitor

I own a PS5 (as well as the soon to be PC) and I want to be able to swap between playing my PS5 on both of them (So when my brother is playing on the TV I can play on the monitor and when he isn't I can play on the TV) and what I've looked into so far has honestly confused me so I need help...

As far as relevant information that (I think) is needed:
- TV: Has a 1920 x 1080 (1080p) resolution with a 60hz native refresh rate and supports up to HDMI 1.4a

- PS5: The model is simply the normal digital PS5 and supports HDMI 2.1 and as far as I can find out supports 1440p and 1080p Monitors/TV's and is maxed out at 120fps/120hz refresh rate

- Monitor: Has a 2560 x 1440 (1440p) resolution with a 200hz native refresh rate but when using HDMI which is supported up to HDMI 2.0 it has a 144hz refresh rate

So what should I get a HDMI Switcher or Splitter and on top of that what features should I look out for so I can do this without increased latency and any other possible problems that could happen?