Follow-up from "Migrate WebHookWorker to use params: step 2"

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The following discussion from !79173 (merged) should be addressed:

• @mkaeppler started a discussion:

  Shared mutable global state makes it really hard to reason about data flow. I know this wasn't introduced in this MR, but this is pretty nasty. Can we think of a better way to accomplish this, such as passing this down the stack to where it's used (the actual hook I presume?)

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