Primal Rights has done a great series (in-depth) on case prep and load development. He tested the impact of timing of annealing in process and its effect on bullet seating force. It was informative and backed up by data in nice graph. Video links below.
Preferred Technique 1
The only step that mattered for consistent, repeatable seating force was to anneal first, tumble and then size. He is not using steel pins, but rather softer media.
Test 1
He tested tumbling first (dirty dirty brass) and then annealing, but the results were definitiely worse (inconsistent and greater seating force curves).
Test 2
He then tumbled to clean brass, annealed, 2nd light tumble to knock down any artifacts/debris (biproduct of annealing) in case neck, and then sized. These results were notably better than Test 1, but not as good as his Preferred Technique. If you are shooting suppressed or using range brass then this is the probably the best procedure.
Impact of Case Prep Order - When to Anneal
Primal Rights - Order of Operations