Thanks for helping me out so far to track the current timelines. I too applied from overseas [US] and got my Adult passport renewal approved within 4 weeks from sending my passport to HMPO. New passport approved on 20th May and arrived on 31st May via DHL. Got text with tracking number on 26th May for the same.
Old passport has my work visa and I need it for re-entry into US. No updates on it until today but got a text from DHL with delivery due on 15th June. So overall, it took another 3 weeks for them to process old passport for return.
DHL tracker with PEX number [without PEX] is useful. It got updated with new waybill number for the old passport on 11th June [information sent to DHL] which gave me hope that they are sending it shortly. Then that information disappeared from DHL website later but got the text on shipment from DHL anyway with same waybill number, if it helps anyone from overseas to track the DHL. https://mydhl.express.dhl/us/en/tracking.html#/track-by-reference