Sonos-like soundbar getting audio via your TV's eArc HDMI plug.
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I have a Yamaha YAS-209. We use our tv as a dumb one with a shield tv plugged into it. The Yamaha allows us to either run the shield signal through it or just have one cable going into the bar from the tv. It also has a subwoofer that connects wirelessly and we have it sitting behind the couch.
It sounds great and works well for what it is. The only problem we have is that when we change volume, there is no visual signal displayed on the screen. We also have a Yamaha receiver for the media room and it does a good job with on screen notifications but the sound bar does not.
I don't have an immediate recommendation, but a number of TVs have audio outputs. We feed audio from our TV to a stereo receiver from the 70s using this method.
Polk, Bose, etc all make something that should work fine. But! If you like tinkering, maybe consider getting a toe in the DIY waters
You've not included your budget, but I think one of the Sonos sound bars would do what you need if you can stretch. The arc is still reviewed as one of the better sound bars out there in terms of sound quality, though the beam is still very good and a bit cheaper.
I don't think you'll find anything in that form factor that mixes the audio between two sources, I'm afraid. For whatever reason, it's tough to find any kind of AV receiver that mixes an HDMI audio signal with another source. That's just anecdotal from my experience though, perhaps someone else knows of some gear that does this.
JBL bar series of soundbars are shockingly good for the price. I avoided soundbars for the longest time because I didn't trust it would be up to my standards but I'm very happy with mine.
As for your record player, I'm sure you're probably aware but it's a very, very low-end record player. Basically toy level. I don't say this to insult you but so you don't get your hopes up on records sounding good on it. If you want good audio from records, next on your list should be upgrading to a nice turntable. Audio technica makes cheap turntables that are decent.
Oh I know it's cheap. I may upgrade one day, but I figure just having better speakers attached would make a big enough difference for now.
HDMI is important as you can control it with the TV remote control. On off too. Essential.
I have a Sony soundbar with a separate, floor standing, Bass unit. If you have a good screen then good bass, I mean really good bass, gives it a cinematic feel. Play the THX Intro on YouTube and you'll know what I mean. My neighbours love it too!
i have a Samsung 990c soundbar on the mantel. wireless sub and surround does me well