Remove vestiges of the old TimeSource implementation & refactor (#2877)

## Motivation and Context
When `TimeSource` was created, we didn't carefully track down all the
places and left a bit of existing implementation to limit the scope of
the change.
## Description
This removes the public (doc hidden) Testing code from
aws-credential-types and our other test time sources instead.


## Testing
- IT/UT

## Checklist
<!--- If a checkbox below is not applicable, then please DELETE it
rather than leaving it unchecked -->
- [x] I have updated `CHANGELOG.next.toml` if I made changes to the
smithy-rs codegen or runtime crates
- [x] I have updated `CHANGELOG.next.toml` if I made changes to the AWS
SDK, generated SDK code, or SDK runtime crates

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Co-authored-by: John DiSanti <jdisanti@amazon.com>