Ethernet vs wireless for HomePod Minis & Apple TV 4K

My Apple TV 4K 2nd gen is connected to the internet via an ethernet cable. A community member posted that it shouldn't matter whether this device is connected via ethernet cable or wirelessly for the successful connection of my 2 HomePod Minis to my Apple TV - as long as my "...router is configured to bridge the wired and wireless as one network." My internet service provider tech set up the router, and I am skeptical that he configured the router as you indicated. Is there an easy way to determine this? Secondly, the post continued that the "...connection between Apple TV and the HomePod mini speakers...is indifferent about the wired, wireless, or combination of both." I find this confusing. Can anyone clarify, i.e., is the Apple TV/HomePod Mini connection truly indifferent to the nature of the internet connection OR is it only indifferent IF the router bridges "...the wired and wireless as one network"? In other words, does the bridging of the router have to occur for the Minis to work? I have tried everything else (including multiple rounds of Apple phone support & many articles) with no luck. I'd really appreciate it if anyone can shed any light as to whether this wired/wireless issue is the likely reason why my 2 HomePod Minis (total of $300 CDN) only work as silent/useless bookends!!