Consider diagnostic bag for ILLink

From @agocke in https://github.com/dotnet/runtime/pull/131911#pullrequestreview-4932999368:

> In general I prefer taking a diagnostics bag vs suppressing warnings. That way the core code stays simple by just adding to the bag, but if the caller doesn't need the bag they can just throw it away after the call instead of passing on the diagnostics

We should consider adopting a pattern like this in ILLink and related tools. This could potentially simplify the suppression logic, but we would need to re-think some of the abstractions around `DiagnosticContext`.

Start with the linked pull request review and trace ILLink's DiagnosticContext and current warning-suppression abstractions. Determine whether the diagnostics-bag pattern fits ILLink and related tools; done means the design question is resolved and the affected abstractions and caller behavior are documented.

Written by the indexing model from the issue text.