I was just about to write a response with this exact sentiment. For me, it's all about defining a contract between the two early, then building to fulfil that contract.
Once the contract is in place, I don't see a significant advantage or disadvantage to starting on either side of the fence.
My go-to tool for creating dummy APIs is json-server. It's much less feature-rich than Swagger, but also much more lightweight.
If you wanna go ever more lightweight, you can paste your JSON on Gist and then just link to that (get the URL via the "Raw" button on top right).
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