Auto merge of #155767 - adwinwhite:eager-norm-outside, r=lcnr

`-Znext-solver` Eager normalization outside of solver 




This PR adds a normalization routine for the next solver that behaves the same as the normalization in the old solver.
The new routine is used to normalize eagerly outside of the next solver.

This is [part 2](https://rust-lang.zulipchat.com/#narrow/channel/364551-t-types.2Ftrait-system-refactor/topic/Eager.20normalization.2C.20ahoy.21/near/582996783) of modifying the next solver to support eager normalization.

Those test changes are mostly wording changes, duplicating some errors or reducing some duplicates. But I could have overlooked something.
Notably it fixes the first, third and fourth examples in rust-lang/trait-system-refactor-initiative#191, but not the second variant.

It's probably easier to review commit by commit.

Fixes rust-lang/rust#151308
Fixes rust-lang/rust#101557
Fixes rust-lang/rust#119692
Fixes rust-lang/rust#136859

Author: bors