No it doesn't. The astro website says it does in the blog post but it doesn't work. I got the adapter and whenever it's added to the chain 120hz is not available. Without the adapter it is.
And here is your 4k solution.
Anyone have an update on the performance / reliability of this product? OP's linked Amazon landing page has 3 out of 5 stars, with reported VRR issues & black screens while using equipment like an Xbox Series X.
Also, it seems the product has been re-listed by the seller (AVFABUL).
I can't tell of any discernible change in the product listing aside from the manufacturer part number, somewhat hilariously re-named:
AV-HAE118 --> AV-HAE118new
For Dolby Digital, this is the first HDMI adapter to support 2.1, for 4K/120: https://www.amazon.com/dp/B0B73P5VX4
A more affordable option is an analog-to-digital converter, but it will only support stereo: https://www.amazon.com/dp/B07W5GNZX5
This is what OP needs: https://www.amazon.com/dp/B0B73P5VX4