Split classes in file.h and value_stores.* to separate files (#3725)

I'm proposing a different split, along the line of "what does this
relate to". I view impl.h as having started down this route. Moving the
inst store stuff to inst.h feels odd to me given how much else is there
right now, but maybe it's still the best approach. Some files only
contain a store, no structured class, but I felt the consistency in file
naming (without _store suffixes) might help.

toolchain/check/handle_binding_pattern.cpp

@@ -5,7 +5,6 @@
 #include "toolchain/check/context.h"
 #include "toolchain/check/convert.h"
 #include "toolchain/check/return.h"
-#include "toolchain/sem_ir/value_stores.h"
 
 namespace Carbon::Check {