Does Persist, Modular, and Hardened Scales give me an infinite loop?
The Arcbound Worker will return with 2 +1/+1 counters and one -1/-1 counter on it, resulting in one +1/+1 counter after state-based actions.

Hardened Scales' ability is not a triggered ability. It is a static ability with a replacement effect, so while it is in play, the Worker will always enter the battlefield with two +1/+1 counters on it; the game will never see the Worker with a single +1/+1 counter on it before state-based actions or other effects are processed.

Therefore, when the Persisted Worker returns to play with Hardened Scales on the battlefield, the Worker will have 2 +1/+1 counters (from Modular and Hardened Scales) and a -1/-1 from Persist. State-based actions cause the -1/-1 and a +1/+1 counter to cancel out, resulting in a Worker with one +1/+1 counter on it before a player gets priority.