functions cannot get user's User-Agent when you call it from hosting emulator by using rewrites

[dora1998]

[REQUIRED] Environment info

firebase-tools: 9.1.0

Platform: macOS

[REQUIRED] Test case

1. Create a project that uses hosting and functions.
2. Call a function from hosting by rewrites.
3. When you test on local emulator, the function cannot get user's User-Agent.

The reproducible sample is below.
https://github.com/dora1998/firebase-tools-ua-example

[REQUIRED] Steps to reproduce

1. git clone https://github.com/dora1998/firebase-tools-ua-example.git
2. yarn install && yarn serve --project YOUR_PROJECT_ID
3. Access to http://localhost:5001/YOUR_PROJECT_ID/us-central1/checkUA, then you'll see your user agent.
4. However, when you access to http://localhost:5000/foobar, you'll see FirebaseCLI/9.1.0 regardless of your User-Agent.

I think this line set the User-Agent regardless of user's one.
https://github.com/firebase/firebase-tools/blob/master/src/apiv2.ts#L203

[REQUIRED] Expected behavior

Functions can get user's UA.

[REQUIRED] Actual behavior

Functions always get FirebaseCLI/9.1.0 as User-Agent on local emulator.

[samtstern]

@dora1998 thanks for reporting this! Seems like a clear bug in our new apiv2 code.

[bkendall]

Sorry I'm so slow in coming to these. Let me take a look.

[bkendall]

Well, that was pretty straight forward to fix. Assuming all goes well, watch for it in a new release of firebase-tools once this is closed.