Bridging the gap between two leases
First, see whether either lease can move. Ask the current home about an extension and the next home about an earlier key date. Even a few days can eliminate a hotel bill and a second move.
If the dates will not meet, choose a short stay near your work, storage, or next neighborhood. Store only what you cannot carry, and keep documents, work gear, medication, and valuables with you.
Build a small budget for overlap, transport, storage, and cleaning. A gap between leases is inconvenient, but it is manageable when you treat it as a brief project with dates, bags, and backups.