Unfortunately, all the variables mentioned do have an impact. IMHE, an improved streamer will make a bigger difference than just adding ethernet vs. wifi. One important part of that change is that most users of betters streamers will be more likely to use a high quality linear power supply on the streamer. Don't underestimate the value of the LPS!
If wiring ethernet through your house isn't an option, powerline adapters that use the copper already routing electrical are a good interim option. Here's an example of the current model of one I used successfully. https://www.amazon.com/TP-Link-AV600-Powerline-Ethernet-Adapter/dp/B00AWRUICG?th=1
Mesh is simply a better WIFI methodology. It still sends wifi through the air and noise degradation is still an issue. I have Eero mesh wifi and it sounds nowhere near as good as wired ethernet (between router, Synology NAS and Sonicorbiter in one room and audio rig including ethernet to opticalRendu in the other room).
I would sum up this thread in order of priority as:
- upgrade the streamer including LPS. Lean towards something compatible with Roon, Squeezebox or OpenHome DLNA/UPnP apps to limit reliance on a small development team.
- use ethernet if possible, powerline adapter otherwise, any wifi as last option.
While the Teac mentioned may be a great choice, I'd think of it similar to integrated amps vs. separate amp/pre. IMHO, I'd prefer separates in anticipation of future DAC upgrades, based on the frequent progress in DACs. YMMV. Cheers,
Spencer