Rollup merge of #109410 - fmease:iat-alias-kind-inherent, r=compiler-errors

Introduce `AliasKind::Inherent` for inherent associated types

Allows us to check (possibly generic) inherent associated types for well-formedness.
Type inference now also works properly.

Follow-up to #105961. Supersedes #108430.
Fixes #106722.
Fixes #108957.
Fixes #109768.
Fixes #109789.
Fixes #109790.

~Not to be merged before #108860 (`AliasKind::Weak`).~

CC `@jackh726`
r? `@compiler-errors`

`@rustbot` label T-types F-inherent_associated_types

compiler/rustc_middle/src/ty/mod.rs

@@ -1004,7 +1004,7 @@ impl<'tcx> Term<'tcx> {
         match self.unpack() {
             TermKind::Ty(ty) => match ty.kind() {
                 ty::Alias(kind, alias_ty) => match kind {
-                    AliasKind::Projection => Some(*alias_ty),
+                    AliasKind::Projection | AliasKind::Inherent => Some(*alias_ty),
                     AliasKind::Opaque => None,
                 },
                 _ => None,