jobs/send_publish_notifications: Add logging calls

[Turbo87]

This can be used to give us a bit more insight into how many emails we are sending out and whether any of them are failing to get sent.

[codecov]

Codecov Report

Attention: Patch coverage is 76.00000% with 6 lines in your changes missing coverage. Please review.

Project coverage is 89.20%. Comparing base (035cae8) to head (bc57341).
Report is 2 commits behind head on main.

Files with missing lines	Patch %	Lines
src/worker/jobs/send_publish_notifications.rs	76.00%	6 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #9357      +/-   ##
==========================================
- Coverage   89.22%   89.20%   -0.02%     
==========================================
  Files         283      283              
  Lines       29073    29091      +18     
==========================================
+ Hits        25939    25950      +11     
- Misses       3134     3141       +7     

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