`tidy` output unorganised and unclear

[Ezrashaw]

A number of issues exist with the tidy tool's output:

• Due to the parallelization, output is mixed between different checks.
• The output itself is not well formatted, Make tidy errors red #106286 took a first step towards fixing this but more is needed.
• There is no standard way to report warnings or other non-fatal information.

@rustbot claim