OREI 8K 2x1 HDMI Switch 4K@120hz - Auto HDMI Selector 48Gbps High Resolution Switch Between 2 Inputs Perfect for Gaming, PS5, Xbox, HDR10, Dolby Vision

I’d recommend this one by OREI. I used it before I got a tv with 4 2.1 hdmi ports. It automatically switches to the input that’s turned on. You also can’t go wrong with UGREEN as someone else said. https://a.co/d/00v6kZr0

Yes you will need a splitter, this is the that I have(https://a.co/d/04Yhxo0R). You are able to get 4k at 120htz. Also think about upgrading your monitors so this won't be something you have to worry about in the future when do upgrade even more things in your setup.