cc @Hilderin

• Related to Grabbing and moving Godot window is laggy on Linux (NVIDIA with Allow Flipping enabled) #39222.

Resizing a window will always be a slow operation with Vulkan as recreating the swapchain takes a while (definitely longer than OpenGL). Since game window embedding is used, Godot has to resize two swapchains every time the window is resized: one for the floating window, and one for the game being embedded (which is a second floating window).

Unfortunately, I don't see a way to optimize this, as a lot of the slowness is down to the OS and graphics driver here. If you switch to the Compatibility rendering method, it should appear to be noticeably faster.

We can however make the slowness less appearant by not requiring the game window to have its resize operation completed before you can see changes to the floating window. This means they will visibly go out of sync during resize operations, but it may be preferable to do this if it means it's smoother to resize the window.

Resizing a window will always be a slow operation with Vulkan

That may as well be true, but I'd profile the resize before making a final judgement! It's always possible there's something else unexpected going on that's eating resources.
I'd do this myself but unfortunately there's no embedding available for my system yet!

After some testing the performance issue was caused by the NOTIFICATION_PROCESS and NOTIFICATION_RESIZED which triggered a deferred call to EmbeddedProcess::_update_embedded_process each frame which was really unnecessarily. I'll create a PR with a fix. It will not affect the re-rendering but rather the unresponsiveness of the window.