`firebase init` error when used in directory of name `project`

### [REQUIRED] Environment info

**firebase-tools:** 14.26.0

**Platform:** macOS

### [REQUIRED] Steps to reproduce

1. Create a directory named `project`
2. Inside said directory, run `firebase init`
3. Select `Extensions` and press enter

### [REQUIRED] Expected behavior

Behaviour should be consistent with using any other directory.

### [REQUIRED] Actual behavior

```
✔ Which Firebase features do you want to set
up for this directory? Press Space to select
features, then Enter to confirm your choices.
Extensions: Set up an empty Extensions
manifest

=== Project Setup

First, let's associate this project directory with a Firebase project.
You can create multiple project aliases by running firebase use --add,

Error: Failed to get Firebase project testing-65ab9. Please make sure the project exists and your account has permission to access it.
coriewatson@Mac project2 % firebase init

######## #### ######## ######## ######## ### ###### ########
## ## ## ## ## ## ## ## ## ## ##
###### ## ######## ###### ######## ######### ###### ######
## ## ## ## ## ## ## ## ## ## ##
## #### ## ## ######## ######## ## ## ###### ########

You're about to initialize a Firebase project in this directory:

/Users/coriewatson/Documents/Invertase/PROJECTS/firebase-extensions/project

✔ Which Firebase features do you want to set
up for this directory? Press Space to select
features, then Enter to confirm your choices.
Data Connect: Set up a Firebase Data Connect
service

=== Project Setup

First, let's associate this project directory with a Firebase project.
You can create multiple project aliases by running firebase use --add,

Error: Failed to get Firebase project testing-65ab9. Please make sure the project exists and your account has permission to access it.

Having trouble? Try again or contact support with contents of firebase-debug.log
```

**--debug**
```
✔ Which Firebase features do you want to set
up for this directory? Press Space to select
features, then Enter to confirm your choices.
Extensions: Set up an empty Extensions
manifest

=== Project Setup

First, let's associate this project directory with a Firebase project.
You can create multiple project aliases by running firebase use --add,

Error: Failed to get Firebase project testing-65ab9. Please make sure the project exists and your account has permission to access it.

Having trouble? Try again or contact support with contents of firebase-debug.log
coriewatson@Mac project2 % firebase init --deb
ug

######## #### ######## ######## ######## ### ###### ########
## ## ## ## ## ## ## ## ## ## ##
###### ## ######## ###### ######## ######### ###### ######
## ## ## ## ## ## ## ## ## ## ##
## #### ## ## ######## ######## ## ## ###### ########

You're about to initialize a Firebase project in this directory:

/Users/coriewatson/Documents/Invertase/PROJECTS/firebase-extensions/project

✔ Which Firebase features do you want to set
up for this directory? Press Space to select
features, then Enter to confirm your choices.
Extensions: Set up an empty Extensions
manifest

=== Project Setup

First, let's associate this project directory with a Firebase project.
You can create multiple project aliases by running firebase use --add,

[2025-11-23T00:48:03.356Z] > command requires scopes: ["email","openid","https://www.googleapis.com/auth/cloudplatformprojects.readonly","https://www.googleapis.com/auth/firebase","https://www.googleapis.com/auth/cloud-platform"]
[2025-11-23T00:48:03.357Z] > authorizing via signed-in user (corie.watson@invertase.io)
[2025-11-23T00:48:03.359Z] Checked if tokens are valid: true, expires at: 1763861266465
[2025-11-23T00:48:03.359Z] Checked if tokens are valid: true, expires at: 1763861266465
[2025-11-23T00:48:03.361Z] >>> [apiv2][query] GET https://firebase.googleapis.com/v1beta1/projects/testing-65ab9 [none]
[2025-11-23T00:48:03.710Z] <<< [apiv2][status] GET https://firebase.googleapis.com/v1beta1/projects/testing-65ab9 403
[2025-11-23T00:48:03.710Z] <<< [apiv2][body] GET https://firebase.googleapis.com/v1beta1/projects/testing-65ab9 {"error":{"code":403,"message":"The caller does not have permission","status":"PERMISSION_DENIED"}}
[2025-11-23T00:48:03.711Z] Request to https://firebase.googleapis.com/v1beta1/projects/testing-65ab9 had HTTP Error: 403, The caller does not have permission
[2025-11-23T00:48:03.798Z] FirebaseError: Request to https://firebase.googleapis.com/v1beta1/projects/testing-65ab9 had HTTP Error: 403, The caller does not have permission
at responseToError (/opt/homebrew/lib/node_modules/firebase-tools/lib/responseToError.js:53:12)
at RetryOperation._fn (/opt/homebrew/lib/node_modules/firebase-tools/lib/apiv2.js:322:77)
at process.processTicksAndRejections (node:internal/process/task_queues:105:5)

Error: Failed to get Firebase project testing-65ab9. Please make sure the project exists and your account has permission to access it.

Having trouble? Try again or contact support with contents of firebase-debug.log
```