[Sentry] Setup performance metrics for send a message

[rlinoz]

Complete this section of the design doc: https://docs.google.com/document/d/1nemsiB9xx16kfJnWfy6kGabsl7FQy_EWAR1lOirEOnE/edit?tab=t.0#bookmark=id.nl2swb59mlsb

[melvin-bot]

@adhorodyski Now this issue is 8 days overdue. Are you sure this should be a Daily? Feel free to change it!

[mountiny]

This is being worked on

[rlinoz]

In the process of getting done

[rinej]

I'm going to work on that issue