Azure App Service is a service used to create and deploy scalable, mission-critical web apps.
I think the first check is whether those early requests actually hit production. The staging slot has its own live hostname, so compare request hosts and per-instance timestamps with the swap activity log. On the source slot, make /ready return 503 until initialization finishes, then 200. Set WEBSITE_SWAP_WARMUP_PING_PATH=/ready and WEBSITE_SWAP_WARMUP_PING_STATUSES=200.
Use swap with preview to test readiness after production settings are applied, before completing the swap.