Camera with 4k hdmi out (livestream) for a TV virtual/faux window

Guys & gals, searched high and low for this online, looking for y'all's help:

Building a virtual window where a camera outputs live hdmi feed to a TV. Like many, our TV is on the fireplace mantel, which blocks a great view out to the back yard.

Need a camera that can stay on for hours with a live hdmi output in 4k (no recording to memory card is necessary), using a wireless hdmi transmitter on the camera, and wireless receiver on the TV.

While GoPro's can record 4k+, live hdmi out is 1080p.

Planning to have it charged/powered by a solar panel charging a powerbank.

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Is it possible to build a camera with great IQ and none of the frills?

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Thanks y'all. For you students out there, check my Youtube for 100+ 360 video on college campuses I did a few years ago.