Add implementation plan for dropping phonenumbers dependency

PLAN.md

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+---
+name: Drop phonenumbers dependency
+overview: Replace the `phonenumbers` library with pure-Python lookup tables for phone-to-timezone inference, eliminating the heavy dependency that causes 8-10s cold starts.
+todos:
+  - id: create-branch
+    content: Create feature branch from main
+    status: pending
+  - id: area-codes
+    content: Create area_codes.py with ~370 NANP area code to IANA timezone mappings
+    status: pending
+  - id: country-codes
+    content: Create country_codes.py with ~200 international calling code to timezone mappings
+    status: pending
+  - id: rewrite-timezone
+    content: Rewrite timezone.py using lookup tables instead of phonenumbers
+    status: pending
+  - id: update-deps
+    content: Remove phonenumbers from requirements.txt, set memory back to 256MB
+    status: pending
+  - id: update-tests
+    content: Update timezone tests to not depend on phonenumbers
+    status: pending
+  - id: deploy-test
+    content: Deploy, test cold start time and Intercom validation
+    status: pending
+isProject: false
+---
+
+# Drop phonenumbers Dependency
+
+## Approach
+
+Replace [packages/intercom/webhook/call_timezone/timezone.py](packages/intercom/webhook/call_timezone/timezone.py) with a self-contained implementation using two lookup tables:
+
+### 1. NANP area code table (~370 entries)
+
+Covers US, Canada, and Caribbean (`+1` numbers). Maps 3-digit area code to IANA timezone. This is the bulk of your call volume and has **high confidence** -- area codes are assigned to specific geographic regions with known timezones. Data sourced from NANPA (public, stable).
+
+```python
+NANP_AREA_CODE_TZ = {
+    "201": "America/New_York",    # NJ
+    "202": "America/New_York",    # DC
+    "205": "America/Chicago",     # AL
+    "206": "America/Los_Angeles", # WA - Seattle
+    "212": "America/New_York",    # NY - Manhattan
+    "303": "America/Denver",      # CO - Denver
+    # ... ~370 entries total
+}
+```
+
+### 2. Country calling code table (~200 entries)
+
+Maps international calling codes (e.g., `44` -> UK, `49` -> Germany) to their primary IANA timezone. For single-timezone countries (UK, Germany, Japan, etc.) this is perfect. For multi-timezone countries (Russia, Australia, Brazil), it picks the most populous timezone and marks confidence as "approximate".
+
+```python
+COUNTRY_CODE_TZ = {
+    "7":   ("RU", "Europe/Moscow"),        # Russia (approximate)
+    "20":  ("EG", "Africa/Cairo"),
+    "27":  ("ZA", "Africa/Johannesburg"),
+    "33":  ("FR", "Europe/Paris"),
+    "44":  ("GB", "Europe/London"),
+    "49":  ("DE", "Europe/Berlin"),
+    "61":  ("AU", "Australia/Sydney"),      # Australia (approximate)
+    "81":  ("JP", "Asia/Tokyo"),
+    "86":  ("CN", "Asia/Shanghai"),
+    "91":  ("IN", "Asia/Kolkata"),
+    # ... ~200 entries total
+}
+```
+
+### Phone number parsing
+
+Simple string parsing of E.164 format -- no library needed:
+- Strip `+` prefix
+- Try matching country code (1-3 digits, longest match first)
+- For `+1` numbers, extract the 3-digit area code and look up in NANP table
+- For others, look up country code table
+
+### What stays the same
+
+- The `infer_timezone()` function signature and return dict shape are unchanged
+- `handler.py` and `__main__.py` remain untouched
+- UTC offset and local time calculation uses stdlib `zoneinfo` (already in use)
+- Tests updated to not depend on phonenumbers
+
+### Coverage quality
+
+| Caller origin | Accuracy | Notes |
+|---|---|---|
+| US/CA (area code known) | Exact | ~370 area codes mapped to specific IANA timezone |
+| Single-tz countries (UK, DE, JP, FR, etc.) | Exact | ~140 countries with one timezone |
+| Multi-tz countries (RU, AU, BR, MX, etc.) | Approximate | Falls back to most populous timezone, marked as "approximate" |
+| Invalid/unknown numbers | Returns None | Same as current behavior |
+
+### What changes in the repo
+
+- Rewrite `timezone.py` with lookup tables (no external imports except stdlib `zoneinfo`)
+- Create `area_codes.py` for the NANP mapping (keeps `timezone.py` readable)
+- Create `country_codes.py` for the international mapping
+- Remove `phonenumbers` from `requirements.txt`
+- Update tests to remove `phonenumbers` assertions
+- Memory limit can go back down to 256MB