https://www.amazon.com/dp/B07KGMPW3C I have this Switch, which I use to connect my Apple TV4K, Switch, PS3, and a “floater” HDMI (for occasional devices, like my NES mini). The reviews are only 3.5 stars, but it was the only inexpensive, 4K @ 60hz switcher I could find. It actually works very well for me.
I also have an older, 5-port HDMI Switch from Monoprice.com. It works great but tops out at 1080p.
Switches are wonderful things. Another piece of tech you might not know about, but is good to know, is “splitters”, which are sort of the opposite of switches. Switches let you hook multiple devices to one display, and switch between which devices is shown on the display. Splitters let you hook up one device, but then show it on however many displays the splitter can handle. It just mirrors the image.
You could also get a simple switch that let's you press a button and changes the HDMI from the TV to one of several other devices on the other side. Like this: https://www.amazon.com/dp/B07KGMPW3C/ref=cm_sw_r_cp_apa_i_NOfDCbJPZQDZM Posting this since you said you could afford a switch but didn't want to switch the HDMI all the time.
You can get switches that can handle 4K at 60Hz (making them future-proof in case you upgrade your TVs at some point) for less than half as much as your device cost and there are even cheaper ones that are equivalent to your device, starting at around 15 bucks. Some of these have more advanced features, like picture in picture. This is quite handy, I've used this to watch over a download on a games console while watching something else on most of the screen, just to name one application (my screen already comes with this feature).
What I noticed is that most manufacturers appear to avoid naming the specific HDMI standard their devices support, at least on shop pages (it's often only in the manuals). However, by looking at the specs and comparing them to this table, it's usually not that hard to figure out which version of HDMI is being supported.
I use this avedio links HDMI Switch with... https://www.amazon.com/dp/B07KGMPW3C?ref=ppx_pop_mob_ap_share with a pc ps4 xbox one and nintendo switch. Examples here https://www.twitch.tv/videos/372050975 watch out for early kh spoilers though.