Long-term planning my living room audio visual setup, considering the options

Modern TV's have no analog connections like SCART, VGA, Component, and many cases even composite (RCA). They have all gone full digital. If you want to connect those kinds of devices to a modern system you need some kind of video processor to perform the conversion. I have a XRGB-Mini Framemeister that I use for this purpose, but these are discontinued. A similar more modern converter would be something like a RetroTINK-4K Pro or RetroTINK-4K CE (same overall input support including VGA, SCART, composite, S-Video, and DV ports, with cable dongles for composite, BNC, and a few specific game consoles (SNES/N64, PS1, and Genesis 2) but less options for processing the video to get the best possible results).

Also the audio on most modern TVs will most likely suck compared to your 2010 TV, as you may still have direct forward firing drivers, but most modern TVs have rear or downward firing drivers (as apparently showing a speaker on a TV is now a deadly sin, performance capability be damned, aesthetics trumps all performance, and besides how could they upsell you their crappy soundbar if they made decent speakers on the TV).

So you will almost certainly need to purchase something like the RetroTINK or similar with your new TV (so factor that into your costs, as they dropped support for analog in part based on the costs, and now you need to add it back in if it was important to you). You didn't really mention the type of TV you had, other than LG (but in 2010 LG had plasma TV's and LCD TVs). I suspect it is plasma if you have not had a serious urge to upgrade it already as the picture quality on the plasma TVs was really outstanding and if it wasn't for 4k resolution and HDR, there really is no reason to replace (LCD's from that era on the other hand would most likely show some serious age against current standards).

If you indeed do have a plasma, really only OLED will look right to you (it won't get as bright full screen as your plasma could, but it is an emissive display tech, so it will seem the most same to you as the plasma does, and give you the increase in resolution to 4k as well as HDR processing capabilities). I'm not normally one to recommend OLED if you are using retro consoles as it can be subject to burn-in, but so too was your plasma if you indeed had a plasma. If you had an LCD, I would recommend sticking with an LCD, and I wouldn't recommend any LCD except for one with 4x HDMI 2.1 ports, so really only a couple Samsung models. It isn't a dealbreaker now that there are HDMI 2.1 external switches available, but that is yet another device you may need in the future and something else that you would need to switch inputs with say a dedicated remote (or preferably some programmable remote like a now discontinued Harmony).

For blu-ray players, I really don't have much to tell you other than to wish you had decided to upgrade about 4-5 years ago. Most of the new stuff still isn't as good as the Oppo UDP-203 in the price range ($550) or UDP-205 is you wanted analog outputs ($1200), and you would need to spend significantly more on a modern one with barely covering the same capabilities. The closest you can get with a modern blu-ray player is the Magnetar UPD-800 or UDP-900, but it is over 3x the cost that you could have had a UDP-203 and UDP-205 respectively: