More new listings also means more choice once you are a firm, qualified buyer, so selling first does not necessarily mean settling, it means shopping from a position where your financing is not in question.
Buying first still works if you have a real cushion to carry two mortgages briefly and a lawyer ready to coordinate both closings, but that is a cash-flow decision, not a market-timing one.
The right order comes down to your own numbers more than the calendar, and a firm sale price is the starting point for that math. Get your hand-reviewed valuation from Joel Dyck.