Get database project

curl --request GET \
  --url https://api.case.dev/database/v1/projects/{id} \
  --header 'Authorization: Bearer <token>'

{
  "id": "proj_abc123",
  "name": "case-mgmt-db",
  "description": "Production case management database",
  "region": "aws-us-east-1",
  "pgVersion": 17,
  "status": "active",
  "connectionHost": "ep-quiet-meadow-123456.us-east-1.aws.neon.tech",
  "storageSizeBytes": 1073741824,
  "computeTimeSeconds": 3600,
  "branches": [
    {
      "id": "branch_main_789",
      "name": "main",
      "isDefault": true,
      "status": "active",
      "createdAt": "2025-01-10T08:00:00Z"
    },
    {
      "id": "branch_staging_012",
      "name": "staging",
      "isDefault": false,
      "status": "active",
      "createdAt": "2025-01-12T10:00:00Z"
    }
  ],
  "databases": [
    {
      "id": "db_neondb_345",
      "name": "neondb",
      "ownerName": "neondb_owner"
    }
  ],
  "linkedDeployments": [
    {
      "type": "compute",
      "id": "app_xyz789",
      "name": "case-portal",
      "url": "https://case-portal.case.systems",
      "envVarName": "DATABASE_URL"
    }
  ],
  "createdAt": "2025-01-10T08:00:00Z",
  "updatedAt": "2025-01-15T10:30:00Z"
}