What you want does exist, but unfortunately is uncommon and therefore more expensive.
One option is to get a device like this that can record to a SD card. What I do is use a laptop with a normal capture card and connect it to my consoles in the living room.
There may be other options that I am not aware of at this moment.
Worth every penny. I recommend looking at my review on Amazon so I don't have to retype it here.
TL:DR, even when (if?) Microsoft fixes 4K capture, I wouldn't have regretted buying it for the major increase in quality and not needing to use a Windows-formatted drive (I have a Mac, and getting my external drive to NTFS was a pain, and I had no way to format it once it inevitably filled up). Last I checked MicroCenter still had them in stock at MSRP.
Amazon has it for 399
I have no idea what is used for HDR, it's footage recorded with the 4k60S+ from Elgato (https://www.amazon.ca/Elgato-Standalone-Recording-Passthrough-10GAP9901/dp/B082N68RNS/ref=sr_1_5?dchild=1&keywords=4k60S%2B&qid=1620670708&sr=8-5) and it's from my Xbox Series X. What I can say is that my computer can't render H.265 using hardware acceleration since it's too old and if I use software encoding it can take up to 16 hours to render a 25 minutes video which is just ridiculous. Hence why I use H.264 also Youtube seems to process H.264 videos a lot faster then H.265 (we're talking days faster) lol
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Edit: added a link to the recorder from Amazon
https://www.amazon.com/Elgato-Standalone-Recording-Zero-Lag-Passthrough/dp/B082N68RNS
This is what I was talking about👍🏻
It all depends on what you want and your budget. If you'd rather connect the capture card through usb for portability sake both the Elgato 4k 60 S+(400$) and the Avermedia Live Gamer Ultra(230$) should work. Though keep in mind the Live Gamer Ultra can only record up to 4k30, while the Elgato goes all the way to 4k60 for an extra 170$.
If you don't mind having to plug the capture card to your PCIe slot then the Elgato 4k60 Pro(250$) or the Avermedia Live Gamer 4k(250$) work pretty much the same for exactly the same price, they both record at 4k60 btw.
£389.99 on Amazon UK but it got the date for Jan 15th
$400. Not too bad, considering something like an Atomos Ninja V is $700.
It's already on Amazon.