How can I connect my TV audio output to my wired HEOS satellite amp? I think I need a Digital Optical Audio>CAT5 converter. If so - any recommendations?

My patio TV (Sony) bit the dust. I've replaced with another Sony.

Old TV: Sound to the patio speakers was controlled via an adapter from the headphone jack that was a 3.5mm>CAT5 cable>Ethernet port

New TV: Doesn't have headphone jack. It does have a digital optical audio jack.

I'm trying to avoid calling/paying my AV company to connect my system. I know, play stupid games, win stupid prizes.....

In total the system was controlled via URC. I have 2 CAT6 connections on the patio. One was used to connect an IR repeater so that signals from a cell phone, tablet, URC remote, etc., could go from the URC brains>ethernet cable>URC IR emitter>tv. Audio was the TV headphone jack>3.55mmToCATcable converter>other ethernet drop.

I'll work on getting the URC controls working later via the TV IP control. I ~think~ my short term of goal of getting sound across my ethernet to the HEOS AMP is the Digital Optical output>ethernet converter widget I asked about in my 1st paragraph.

Equipment: Sony X80K television, Denon Heos HS2

Edit to add - I have an unused COAX alongside the 2 CAT6 cables in my drop. I'm trying to use the existing wiring/jacks without having to rewire the COAX end. It is a 3rd option at the drop-site though if that matters.

The audio is likely on the hdmi cable and dongle to extract it 3.5mm jack and use with your old infrastructure is cheap and widely available.
Not exactly sure the location of all your devices but you might be able to do hdbt to accomplish this also. Multiple vendors but the monoprice stuff works well.

Converter
Cable

Have to be able to set the output to PCM instead of digital, which I think your TV does. If not Amazon return is easy.

Can't guarantee it'd work, but guessing.

I have a couple options. email me and I can likely find something that works for less than retail .