Your TV is too old (from 2013). You might be able to get 5.1 audio from 1 or 2 of the TV’s native apps like VUDU but that’s about it. You either need to upgrade your TV or add an eARC adapter like the HDFury Arcana that will allow any external media device to bypass your TV’s limitations and send audio directly to the Arc.

would something like this work? Don’t want to spend $600 on the eArc.

would something like this work? Don’t want to spend $600 on the eArc.
Not really. You would need to connect that via optical withe the Sonos adapter, which only gives DD 5.1. If you wanted anything above that; DD+, Atmos, Dolby HD, you will need an eArc extractor (and they aren’t inexpensive)
Only if you use the optical output.
Probably the TV is too old, but you should make sure that Anynet is enabled on the TV.