How about websites just straight up aren't allowed to physically hurt me, by default?
You asked “which web browsers have a setting to tone map HDR images such that they look like SDR images?”; I answered. Were you not actually looking for a solution?
I was looking for a setting, not a hack.
Web sites aren’t made for just you. If images from your screen are causing you issues, that is a you / your device problem, not a web site problem.
I agree, it's not a web site problem. It's a web standards problem that it's possible for web sites to do that.