I’ve done this (different products though) a few times.
biggest stumbling blocks initially will be, once you get a solution running; timing differences.
I’d be keen to put something inline to help split the signal, ie two analogue streams (super easy, probably working with 2x 3.5mm plugs, and using a splitter (will halve signal level)), and then use the soundbars ANALOGUE INPUT (assuming has one, apologies for lack of research)…
running two analogue feeds is best bet to overcome timing differences.
streaming 2x via bluetooth is becoming a technology ‘thing’; but if different products receive, processing times being different, leads to audio issues…
ie my two DAPs that receive bluetooth take slightly different millisecond amounts (by a factor of hundreds of ms), and any solution that feeds them both simultaneously will lead to playback issues.
running bluetooth to soundbar, or arguably, ‘digital anything’ (eARC/toslink), might have a processing delay.
generally speaking, an analogue input has fastest processing and could prove most usable technology.
setting TV to PCM output (rather than auto/surround sound) on the digital out, and a few DAC options could then be engaged to make you a high(er) quality analogue feed.
I presently run a fiio M11+ (DAP) into an old AudioGd DAC that then feeds a box that redigitises the signal.
the sound is amazing.
having done the same, for years, veing an iFi Diablo into some Sennheiser RS170 ‘wireless headphones’; also redigitising the signal- a nice outboard DAC will make for an excellent source even if it has to be redigitised.
I say this, and give my use cases simply to have pundits consider their options from a wider pool of resources.
The AudioGD DAC I use in ‘b setups’ was an old bit if kit gathering dust at a mates place. (and has multiple outputs and supports plug types I use).
I have found a Fiio BTA30 /BTA30 Pro indespensible when trying to do oddities with setups or walking off the well troden hobby path.
bluetooth in and out/DAC (digital in into analogue out) functions, and ability to reroute signals in ways that I wish ‘very handy’.
(also can DAC out direct from Nintendo Switch and Playstation 4/5 etc)(not much does that, generally requires UAC1 USB modes)
thinking, if sony soundbar has analogue input, an inbetween TV and amplifiers (soundbar AND Naim) stage splitting analogue to two feeds will sidestep a tonne of synchronisation/timing issues…