I think processing may mean there is an issue, so best to ring them up. Ours was a child renewal send 5th May, got it back in just under 3 weeks. It went from old passport received to approved without going through the processing status. If you’re going on holiday fairly soon I would ring them as it’s likely to be in a pile with a query on it, and of course they don’t know if/when people are needing it so not done in priority.