This appears to happen in ALL bedrock versions since 1.16. Skeletons will shoot almost instantly if you run away from them and losing their sight, and will shoot when you come at their sight. When you hit, damage, or get too close, it will shoot way faster and it is very inconsistent.
This is very annoying.
Thank you for your report!
We're tracking this issue in MCPE-61036, so this ticket is being resolved and linked as a duplicate.
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