Importing files doesn't work on Vercel deployment

I created a minimal reproducible example.

This repository was started by running bunx create-frog -t vercel. Then the only change I did was extract the actual rendering of the frame into a separate file.

This all works fine when running bun run dev locally.

However, after deploying to Vercel (by running bun run deploy), the serverless function is crashing.

This is the full error log from Vercel

Error: Cannot find module '/var/task/api/Frame.js' imported from /var/task/api/index.js
    at new NodeError (node:internal/errors:405:5)
    at finalizeResolution (node:internal/modules/esm/resolve:332:11)
    at moduleResolve (node:internal/modules/esm/resolve:1029:10)
    at moduleResolveWithNodePath (node:internal/modules/esm/resolve:876:12)
    at defaultResolve (node:internal/modules/esm/resolve:1242:79)
    at ModuleLoader.defaultResolve (node:internal/modules/esm/loader:403:12)
    at ModuleLoader.resolve (node:internal/modules/esm/loader:372:25)
    at ModuleLoader.getModuleJob (node:internal/modules/esm/loader:249:38)
    at ModuleWrap.<anonymous> (node:internal/modules/esm/module_job:76:39)
    at link (node:internal/modules/esm/module_job:75:36) {
  url: 'file:///var/task/api/Frame.js',
  code: 'ERR_MODULE_NOT_FOUND'
}
INIT_REPORT Init Duration: 284.92 ms	Phase: init	Status: error	Error Type: Runtime.ExitError
Error: Cannot find module '/var/task/api/Frame.js' imported from /var/task/api/index.js
    at new NodeError (node:internal/errors:405:5)
    at finalizeResolution (node:internal/modules/esm/resolve:332:11)
    at moduleResolve (node:internal/modules/esm/resolve:1029:10)
    at moduleResolveWithNodePath (node:internal/modules/esm/resolve:876:12)
    at defaultResolve (node:internal/modules/esm/resolve:1242:79)
    at ModuleLoader.defaultResolve (node:internal/modules/esm/loader:403:12)
    at ModuleLoader.resolve (node:internal/modules/esm/loader:372:25)
    at ModuleLoader.getModuleJob (node:internal/modules/esm/loader:249:38)
    at ModuleWrap.<anonymous> (node:internal/modules/esm/module_job:76:39)
    at link (node:internal/modules/esm/module_job:75:36) {
  url: 'file:///var/task/api/Frame.js',
  code: 'ERR_MODULE_NOT_FOUND'
}
INIT_REPORT Init Duration: 359.00 ms	Phase: invoke	Status: error	Error Type: Runtime.ExitError
Error: Runtime exited with error: exit status 1