[clang][fat-lto-objects] Make module flags match non-FatLTO pipelines (#83159)

In addition to being rather hard to follow, there isn't a good reason
why FatLTO shouldn't just share the same code for setting module flags
for (Thin)LTO. This patch simplifies the logic and makes sure we use set
these flags in a consistent way, independent of FatLTO.

Additionally, we now test that output in the .llvm.lto section actually
matches the output from Full and Thin LTO compilation.