Update: Godot 4.0 features a basic OpenGL ES 3.0 renderer (which uses WebGL 2.0). This renderer is sufficient to render most 2D projects and some 3D projects correctly. This renderer will receive further development in future 4.x releases.
As a result, you can now export Godot 4 projects to HTML5 like you could with Godot 3.x. There is a hard requirement on SharedArrayBuffer though, unlike in Godot 3.x. (The upside is that this allows for using threads and low-latency audio, which is otherwise not possible without severely limiting the feature set of the audio engine once exported to HTML5.)
Old answer is kept below for posterity.
Godot 4.0 does not support HTML5 export yet, as the OpenGL renderer (required for WebGL) isn't finished yet. WebGPU is far from being finalized, which means it'll be years until the Vulkan renderer can run in HTML5 in some form.
We don't expect the OpenGL renderer to be finalized for Godot 4.0's release, but rather for a future 4.x release. Therefore, Godot 3.x will remain supported for a certain amount of time after Godot 4.0 is released (at least until 4.1 is released).