@sd13 I have got last year a Yamaha YHT 4940 (basically a RX-v483+ 5.1 included speakers). All Yamaha RX-v*83 (from last year, like
this RX-v383 at $219) have 4 HDMI In - 1 HDMI Out all supporting HDCP 2.2 and HDMI 2.0, HDMI ARC and HDMI CEC (Bravia Sync to use the HDMI devices' remotes) obviously included. The new models should be RX-v*85.
My Bravia doesn't support Dolby Vision, but last Christmas the Yamaha AVR have received a FW update for it (and I have read it works). Also it supports HLG and HDR10 and BT.2020. These latter all work fine with the cheap HDMI cables I have got from Amazon. The audio is also great for that price.
Instead, if I was you, I'd double check about Dolby Vision on Bravia. The last time I checked only the Apple TV was compatible via HDMI. Not even the Sony UHD Blu Ray was supported, due to a specific DV profile Sony uses in the Bravia. Oh, and Android TV in the Bravia is awfully slow. Slow even changing the volume, to be clear.
PS: With that configuration you would still have a 5th HDR HDMI port available on the TV (the other must be used by HDMI ARC). The audio would go from the HDMI device to the TV back to the AVR via HDMI ARC, so it won't support all formats (like AAC 5.1, nor DTS since it is currently broken in Android TV for Bravia. Forget about HiRes audio). Since you said you don;t care much about audio it shouldn't be an issue!