The original reason I wanted to do this was so that we can replace
the Android-specific code with this in the future, but of course,
just deduplicating between DolphinWX and DolphinQt2 is nice too.

Fixes:

- DolphinQt2 showing the wrong size for split WBFS disc images.

- DolphinQt2 being case sensitive when checking if a file is a DOL/ELF.

- DolphinQt2 not detecting when a Wii banner has become available
after the game list cache was created.

Removes:

- DolphinWX's ability to load PNGs as custom banners. But it was
already rather broken (see https://bugs.dolphin-emu.org/issues/10365
and https://bugs.dolphin-emu.org/issues/10366). The reason I removed
this was because PNG decoding relied on wx code and we don't have any
good non-wx/Qt code for loading PNG files right now (let's not use
SOIL), but we should be able to use libpng directly to implement PNG
loading in the future.

- DolphinQt2's ability to ignore a cached game if the last modified
time differs. We currently don't have a non-wx/Qt way to get the time.

GameFile: don't store file path parts

Currently, GameFile returns a generic banner if the file didn't have one
available (either because the file format doesn't support it, or because
it's a Wii file without an associated save).

It makes more sense to handle the lack of banner in the UI layer. The
game list will use the generic missing banner explicitly (no change from before), and the game info window now omits the banner display entirely if the file didn't have one (since it's not useful to display/allow the user to save the "missing banner" banner).