Using `clang-tidy`'s `modernize-use-default-member-init` check and
manual review of the changes, and some extra manual changes that
`clang-tidy` failed to do.
Also went manually through all of `core` to find occurrences that
`clang-tidy` couldn't handle, especially all initializations done
in a constructor without using initializer lists.
It changed name as part of the DisplayServer and input refactoring
in #37317, with the rationale that input no longer goes through the
main loop, so the previous Input singleton now only does filtering.
But the gains in consistency are quite limited in the renaming, and
it breaks compatibility for all scripts and tutorials that access
the Input singleton via the scripting language. A temporary option
was suggested to keep the scripting singleton named `Input` even if
its type is `InputFilter`, but that adds inconsistency and breaks C#.
Fixesgodotengine/godot-proposals#639.
Fixes#37319.
Fixes#37690.
