Ask HV: multi-room audio/video, preferably IP-based

Any advice for how to do multi-room (whole-house) audio and video? That is being able to distribute a source (audio/video) to multiple rooms in a residence. This might be mostly for music, but sometimes you want to distribute video: For example watch the same movie in the living room and kitchen while preparing dinner.

Requirements:

* Use Cat6 cables between rooms, not HDMI.

* One-to-many - i.e. watch the same program (or listen to the same music) in multiple rooms.

* Forward USB keyboard/mouse. For plain A/V just supporting IR signal forwarding might be OK, but keyboard/mouse forwarding works for A/V and computers.

Strongly desired:

* Should support at least 4K 30Hz.

* Prefer standards, and avoid single-vendor solutions. A single-vendor solution may be acceptable if vendor is solid and well-established.

* Any device with HDMI output (encrypted or not) can be usable as an input (source). This includes sharing a laptop screen.

* Output can be any TV/monitor or A/V receiver or soundbar with HDMI input.

* Be able to share A/V and IP data over the same Cat6 cable.

* Prefer if inputs don't all have to be a single central location. Ideal is that any "satellite" (non-central) location can switched between input and output. However, that may not be realistic.

* Should support at least 2 (and preferably 4) independent distributed "channels". Any output should be able to select any of distributed sources as well as local non-shared sources (like a laptop). It is probably fine to hook up each shared stream and each local device to the HDMI inputs of the monitor/soundbar and use the "input" or "source" on the monitor/soundbar (or remote) to switch.

* Ok if video is compressed or not 100% synchronized, but any lags should be small and hard-to-notice, especially if not all the same.

* Bonus if using WiFi is an option (even if reduced quality).

* CEC pass-though is a plus.

Resources:

I like the concepts of SDVoE (Software Defined Video-over-Ethernet) - https://sdvoe.org/. I like the idea that the central "crossroads" unit is just a fast Ethernet switch. However, it seems very much focused on business rather than residential uses, and requires 10G Ethernet.

HDBaseT doesn't seem quite as elegant, but seems a little more accessible for residential installation.

I also see a number of "HDMI over IP" solutions. Unclear if they adhere to any standards. It's hard to find something that supports both one-to-many and keyboard/mouse forwarding. The former seem to be intended for AV while the latter is more intended for KVM applications. Something that works well for both would be preferable.