Not a consultant but from what I've seen, being on restoration status means you're technically out of status and restoring it. You can apply for a study permit during this time, but the challenge is that you'd need a valid acceptance letter from a DLI first, and IRCC may question why you're switching from work to study after a refusal.
I'd honestly recommend talking to a licensed immigration consultant on this one since the interaction between restoration, refused extensions, and new study permits is tricky and getting it wrong could affect your future applications.