Upgrading From R9 380

I build my machine a number of years ago with a Core i5 6600 3.3Ghz, 16GB DDR4 2133, MSI B150 ITX Motherboard, Radeon R9 380 Video Card, Samsung 850 EVO 256GB SSD, Corsair 600 Watt PSU, Thermaltake Core V1 ITX Cuve Case.

Its my living room HTPC/Plex Server/Emulation machine. I have Xbox Game Pass and use an Xbox controller to play a couple of games, mainly Overwatch but really dont play any new games on it anymore as I play my games on my Xbox One X.

I upgraded to a 4K Vizio TV from an older 1080P screen and now my Sapphire Radeon R9 380 is getting long in the tooth in both performance, and the fact that its HDMI port is not 2.0 capable so I am locked to 4K 30 Hertz maximum. I am limited on length of video card as I have the Thermaltake Core V1 Cube case and it has a maximum GPU double wide length of 260mm inside the case but has a little cutout to extend to the front panel for a maximum length of 285mm, however Im sure any sort of power connection in that last 25mm may interfere so I would prefer to stay 260mm or less just to be safe.

What would be the best card for me to upgrade to gain HDMI 2.0, Fit the length requirement, and better performance then what I currently have?

You can look at something as Vega 56 the prices should be around $250. Need to double check on size L 27.4 cm H 13cm W 5cm for Gigabyte Radeon RX Vega 56 Gaming OC 8GB

That should work with HDMI 2.0b. This one might not be the one that fits your case but you should be able to get something that would fit within Vega 56 range ...

Zotac, Gigabyte, and MSI all make "mini" ITX version of the RTX 2070 (and other models below the 2070). They are well under your 260mm requirement and have HDMI 2.0 (not sure on the b spec)