my_sea.html: persist burger + bud btns across all 3 phases — TDD

Bud + burger now render unconditionally on /gameboard/my-sea/ alongside the always-on gear-btn (was sprint-6c) + base-html kit-btn. Persists through sign-gate, landing, and picker phases so the user can reach the cross-cutting menu / invite affordance from every state.

## templates/apps/gameboard/my_sea.html

3 new includes/scripts placed at the bottom of `<div class="my-sea-page">` alongside the existing `_my_sea_gear.html`:
- `_my_sea_bud_panel.html` — bud btn + slide-out (POSTs to `my_sea_invite` stub, same shape as on my_sea_gate.html)
- `_burger.html` — burger btn + fan of 5 sub-btns
- `<script src="...burger-btn.js">` — the delegated click + flash handler

All unconditional (outside the if/else nesting that branches on user_has_sig / show_picker), so they survive every phase transition.

## apps/gameboard/tests/integrated/test_views.py

3 new ITs on MySeaViewTest — one per phase:
- `test_my_sea_renders_bud_btn_and_burger_in_sign_gate_phase` (no significator)
- `test_my_sea_renders_bud_btn_and_burger_in_landing_phase` (significator set, no draw)
- `test_my_sea_renders_bud_btn_and_burger_in_picker_phase` (significator + empty MySeaDraw row + ?phase=picker)

Each asserts both `id="id_bud_btn"` + `id="id_burger_btn"`. Sign-gate phase also asserts burger-btn.js loaded.

## Verification

All 215 gameboard IT+UT green (+3 new). No JS / model touches; pure template additions.

Code architected by Disco DeDisco <discodedisco@outlook.com>
Git commit message Co-Authored-By:
Claude Sonnet 4.6 <noreply@anthropic.com>

src/templates/apps/gameboard/my_sea.html

@@ -1065,5 +1065,11 @@
         {# (sign-gate / landing / picker). NVM-only menu mirrors the    #}
         {# gatekeeper's gear; "back out to /gameboard/" affordance.     #}
         {% include "apps/gameboard/_partials/_my_sea_gear.html" %}
+        {# Bud + burger persist across every stage too — same affordance #}
+        {# as on the my-sea gatekeeper, so the user can invite + reach   #}
+        {# the cross-cutting menu from sign-gate / landing / picker alike.#}
+        {% include "apps/gameboard/_partials/_my_sea_bud_panel.html" %}
+        {% include "apps/gameboard/_partials/_burger.html" %}
+        <script src="{% static 'apps/epic/burger-btn.js' %}"></script>
     </div>
 {% endblock content %}