In the calmest possible voice - I've done all this, yet it will not share my music library with my apple tv

I've done all this

Unfortunately this gives us no clue to what you have tried, and what the outcome was. Expect some suggestions that you may have tried already. 🤷‍♂️ Writing an effective ASC question - Apple Community

yet it will not share my music library with my apple tv

Home Sharing is for sharing items in your (music) Library from a computer (not from iPhone or iPad). What computer do you have there [1], with what version OS [2]?

Also, what is your model Apple TV box?

Identify your Apple TV model - Apple Support

Find your Apple TV model number - Apple Support

- Home Sharing is for sharing on a single home network (not over the internet), with compatible devices, and compatible media formats. All devices must be on and running.

- Apple Music subscription content is not available for Home Sharing. Apple Music content is meant to be streamed from Apple’s servers, not locally.

- Home Sharing content will become available in the Computers app on Apple TV (not in the Music app on Apple TV).

- Home Sharing requires that this service uses the same Apple ID account on both the source computer and the playback device.

- Home Sharing has on on-off setting. Verify that the service is active.

However I see in your response I won’t be able to get the subscription Apple service.

For Apple Music subscribers, they can get Apple Music subscription content on the Apple TV box (through the Music app), for the 2015 model or later. That would not use the local sourcing as used by the Home Sharing function, though.

AirPlay might be a viable alternative option, perhaps?

Use AirPlay to stream audio - Apple Support

Local streaming like Home Sharing, but you operate it on the source device instead of destination device.

if it was me then I would provide more info about

your setup

what generation of appletv? and appletvOS version?

what computer operating system and version?

how are the computer and appletv connected to the router?

does other things works like remote app and airplay and the likes?

does other devices such as your signature iphoneXS able to communicate with the appleTV even if the appletv is not able to communicate with the computer?

what maker and firmware model is the router?

if it's wired ethernet have you tested with other cables?

This is a user helping users with tech questions forum, we are not apple and apple do not read your posts here

it's sort of like you going into an apple store asking adwise from other customers inside

we don't get paid we braindstorm and try to help people troubleshoot to try and aid them in their ills