given nvidia having a better performance to cost ratio,

In what part of the world? I haven't found that to be true.

the power usage (big one for a compact living room system),

You might want to do some more homework in this area. I recall AMD having better performance/watt in the tests I read before buying, but it's hard to declare a clear-cut winner, because it depends on the workloads you use and the specific cards you compare. AMD and Nvidia don't have exactly equivalent models, so there's going to be some mismatch in any comparison. In stock configurations, I think both brands were roughly in the same ballpark.

Departing from stock, some AMD users have been undervolting their cards, yielding significant power savings in exchange for slight performance loss. Since you're planning a compact living room system, you might want to consider this. (I don't know if Nvidia cards can do this at all, or whether their drivers allow it.)

Regardless of brand, you can also limit your frame rate to reduce power draw. I have saved 30-90 watts by doing this in various games. Not all of them benefit much from letting the GPU run as fast as it can.

and the fact that they have the potential for HDMI2.1 support which AMD doesn’t have a solution to yet.

AMD cards do support HDMI 2.1. Did you mean Fixed Rate Link features, like variable refresh rate, or uncompressed 4K@120Hz? You're not going to get that natively with any open-source GPU driver, because the HDMI Forum refuses to allow it. Most people with VRR computer displays use DisplayPort, which doesn't have that problem (and is better than HDMI in nearly every other way as well). If you really need those FRL features on a TV, I have read that a good DisplayPort-to-HDMI adapter will deliver them.

Another thing to consider: How much VRAM is on the AMD card vs. the Nvidia card you're considering? I've found that even if a card with less VRAM does fine with most games when it's released, it can become a painful constraint over time, leading to the cost (and waste) of an early upgrade even if the GPU itself is still fast enough for the next generation of games.

I switched from Nvidia to AMD, and have not been sorry.