How to change focus-mode: mouse's delay?

You can change this by disabling the option focus-change-on-pointer-rest in schema org.gnome.shell.overrides (which overrides the original option in org.gnome.mutter while GNOME Shell is running).

But note that this might actually have more downsides than you expect.

When this option is enabled, there is a hardcoded delay of 25 milliseconds "to check whether the pointer has stopped moving after a crossing event", added in commit 59bc5b7 in response to bug report 678169.

commit 59bc5b7975f1f19ebacb520c1c2666c0828d1111

display: (Optionally) delay focus changes in focus-follows-mouse mode

Moving focus immediately on crossing events as we currently do
in focus-follows-mouse mode may trigger a lot of unwanted focus
changes when moving over unrelated windows on the way to a target.
Those accidental focus changes

 - prevent features like GNOME Shell's application menu from
   working properly

 - and are visually expensive since we now use a very distinct
   style for unfocused windows.

Instead, delay the actual focus change until the pointer has stopped
moving.

(Commit message reformatted to emphasize the reasons.)

$ gsettings set org.gnome.mutter focus-change-on-pointer-rest false

This worked for me in Gnome 3.30.