Using apple tv 1st gen.

I wasn't referring to your music system, only the Apple TV. Those systems are built for longevity, and I agree they do have great audio capabilities. However, the Apple TV is essentially a computer and is now over 12 years old. Syncing was only available on that model so it was eventually removed from iTunes, I can't speak to the fact of if it was also from older versions but refraining from updating isn't really a good idea anyway. The fact that it's still in working condition is a testament to that hardware. However, even if you were able to get it to sync again other issues will arise sooner rather than later.

You would still be able to retain most of that function with a current Apple TV. You could use an audio extractor to connect with your sound system while the Apple TV could be setup with iCloud photo library to show slideshows, or you could use a client to stream contents from your NAS (photos and music).

If you really have an Apple TV (1st generation), the white/aluminum 7.7" box from 2007, then these are now considered obsolete, meaning Apple has discontinued all hardware service.

Access to the iTunes Store from that model device is also discontinued, but that doesn’t seem to apply here, as you didn’t want that anyway.

Not updating iTunes to the latest version might be a good thing in this case, as current versions of iTunes (12.7 or later) do not connect to the Apple TV (1st generation) anymore. Earlier versions should be able to connect and sync content, afaik.

Then maybe something has changed, perhaps someone who still has a working 1st gen and is using an older version of iTunes can weigh in. However it may just come down to it being EOL, it is over 12 years old at this point.

That article strictly refers to accessing home sharing through IOS. Home Sharing itself, within iTunes on your Mac/Pac, is still very much intact and I use it regularly.

You would not need a lot of equipment to setup an equivalent. It would simply require an audio extractor to connect to your sound system, as I explained above. The only thing you would be losing would be the ability to sync content, but as I said you would simply setup a client on the Apple TV (there are various apps available for this) that would enable you to stream directly from your NAS to Apple TV

As I said the 1st gen was the only product that could sync, all other models are streaming only. Apple removed that function from current versions of iTunes as it didn't make sense to keep that feature on a product that had long been classified as obsolete and didn't have a big user base. Not sure why it isn't working on the version you have, but my point was that even if you were to get that working again it is only a matter of time before it starts to fail, it is already 12 years old and while your other gear may still work you can't expect this type of device to last much longer. Most users have already started to experience failure. It is best to start considering a replacement. There are other devices, but if you want something akin to Apple TV that won't exist elsewhere.

The 1st gen doesn't have access to Netflix or any 3rd part content nor any features of the other models (i.e. airplay). It initially had Youtube, but google removed that when they updated their API.