No, no browser supports H.265. And wide support is not likely to be added in the near future.
EDIT:
I updated the question because there are reports of it working in Edge when hardware decoding is available.
This is a good point.
In this case, the browser still does not support it. It is offloading decoding to the OS (Windows), and the OS is offloading to the hardware. But the result is the same as having browser support. This becomes cheaper, because the license was paid for by the chip company.
Background:
H.265 licensing has historically been extremely expensive. In some cases orders of magnitude more expensive than H.264. MPEG-LA and HEVC Advance patent pools expected companies like apple and Microsoft to pay for it. But they got too greedy (specifically HEVC Advance) by eliminating price caps, so Microsoft would have had to pay hundreds of millions of dollars for H.265, where H.264 caps out in the low millions. HEVC Advance has changed the licensing policy, but it may be too late, as google Microsoft, Amazon, Netflix, Cisco, Mozilla and others are developing a royalty free alternative (under the name Alliance for Open Media) so online video can never be held hostage again.