Minimum reproduction of middleware to middleware rewrite bug

• Site1: https://next-middleware-to-middleware-bug-repro-site1.vercel.app/ (target)
• Site2: https://next-middleware-to-middleware-bug-repro-site2.vercel.app/ (middleware proxy to target)
• Site3: https://site3.danny-312.workers.dev (baseline: cloudflare worker proxy to target)

Site1 is the parent site, and site2/site3 are the child sites

In production, site1 is a multi-tenant vercel project, which we're mocking in this repo with a single tenant.

/tenant/[num].tsx renders the tenant-specific content. In production, this is /[tenant]/[[...path]].tsx /basepath/* is rewritten to /tenant/* inside site1, where /basepath/ is arbitrary and defined by the customer. /basepath/* is rewritten to $SITE1_ORIGIN/basepath/* inside site2 and site3.

Bug reproduction

1. navigate to site2
2. click the link to /basepath/0
3. click the num++ and num-- buttons to increment and decrement the number
4. observe that Application error: a client-side exception has occurred (see the browser console for more information). is logged in the browser console

Expected behavior

1. navigate to site3
2. click the link to /basepath/0
3. click the num++ and num-- buttons to increment and decrement the number
4. observe that the number is incremented and decremented correctly using client-side routing (no page reloads)