What you want is a called a 'Multi-Viewer'.
Similar to this and up from there depending on needs/reliability you are looking for.
https://www.amazon.com/Multi-Viewer-Switcher-Seamless-Support-Security/dp/B07H5TF6X2
A multiview box: https://www.amazon.com/dp/B07H5TF6X2 There are cheaper and more expensive. Probably all kinds of quirks and limitations and no mention of input lag..