This was attempted to be fixed by frenzibyte using some hack workaround
logic, but this is the true fix.
Things were never matching due to `UpdateSize` spamming `Resize`
transforms every frame, causing the fade out to complete before
transforms have reached a final state.
These aren't used in many places, but we've since moved away from
opacity in UI elements like this, so let's just nuke it here for
legibility.
Addresses https://github.com/ppy/osu/discussions/29906.
I've also removed inheritance from `SearchTextBox` because it contains
logic that might interfere with the internal implementation of dropdown
search bars (focus logic and stuff).