Update `SessionDiagnostic::into_diagnostic` to take `Handler` instead of `ParseSess`
Suggested by the team in [this Zulip Topic](https://rust-lang.zulipchat.com/#narrow/stream/336883-i18n/topic/.23100717.20SessionDiagnostic.20on.20Handler).
`Handler` already has almost all the capabilities of `ParseSess` when it comes to diagnostic emission, in this migration we only needed to add the ability to access `source_map` from the emitter in order to get a `Snippet` and the `start_point`. Not sure if adding these two methods [`span_to_snippet_from_emitter` and `span_start_point_from_emitter`] is the best way to address this gap.
P.S. If this goes in the right direction, then we probably may want to move `SessionDiagnostic` to `rustc_errors` and rename it to `DiagnosticHandler` or something similar.
r? `@davidtwco`
r? `@compiler-errors`
4d830b7775