Move DocAuthLog registration out of shared analytics class

[zachmargolis]

• Builds on logging added in Add logging ahead of removing Analytics logic #7864, and is a redo of Remove event-specific hooks in Analytics class, move up to calling code #7685 now that we have logging to ensure better coverage
• Specs were added in Add logging ahead of removing Analytics logic #7864

Cloudwatch query to verify results

• production.log

fields @timestamp, @message, @logStream, @log
| filter name = 'event_to_doc_auth_log_token'
| sort @timestamp desc
| stats count(*) by source, token, action, success

Results show an exact match between original and proposed giving me a high level of assurance this change should work this time:

[solipet]

Looks good! Independently verified via the query that the old/new messages are one-to-one.

[zachmargolis]

Looks good! Independently verified via the query that the old/new messages are one-to-one.

Thanks for verifying, Doug! <3