feat(web): move the chat action cluster to the pinned bottom and align the button sets

- task 01: relocate the .chat-actions row (New chat + Share, comments byte-identical with a Phase 65 note) from the top of the column to the bottom of .chat-shell, directly above the composer
- task 02 (owner-locked A1): wrap the row + #composer in ONE sticky .chat-bottom unit (position: sticky; bottom: env(safe-area-inset-bottom, 0), no z-index) — the pills stay at the bottom of the screen at every scroll position and settle into flow above the footer
- task 03 (owner-locked A2): right-align the bottom row to the column's right edge (justify-content: flex-end), mirroring the right-aligned Save-as-doc corner; the five action pills share one 44px / 999px-pill geometry
- task 04: dedicated Playwright suite tests/e2e/test_bottom_chat_actions.py (resting geometry, the A1 pin across the sticky range, A2 alignment + DOM order + mobile stack + 360px overflow bound + 44px touch targets, New chat / Share click-through) — green in isolation
- task 05: regression matrix green in isolation (pinned_composer 4, save_share_ux 5, chat_persistence 4, share_chat 4, chat_history 5, smoke 3); full gate green — unit + integration pass, app/ coverage 99% (>90%), ruff + pyright clean

tests/unit/test_save_chat_ui.py

@@ -393,9 +393,12 @@ def test_share_button_ships_visible_beside_new_chat() -> None:
     "Share chat", SHIPPED VISIBLE to every visitor (phase 55 task 03 —
     NO ``hidden`` attribute, no reveal step; the phase-51 admin-only
     ship-hidden gate is gone), BESIDE #new-chat-btn in .chat-shell
-    inside <main>, above #messages — the chat-shell actions read as a
-    pair (New chat | Share; the Save pill is gone, phase 55). No other
-    page carries it (chat-page only, like New chat)."""
+    inside <main> — the chat-shell actions read as a pair (New chat |
+    Share; the Save pill is gone, phase 55). Phase 65 (2026-09-01,
+    ``TODO.md`` L3, owner confirmation) moved the row from the top of
+    the column to the bottom: below #messages, directly above the
+    composer. No other page carries it (chat-page only, like New
+    chat)."""
     html = _index()
     btn = re.search(r'<button[^>]*id="share-chat-btn"[^>]*>', html)
     assert btn, "index.html must contain #share-chat-btn"
@@ -408,13 +411,18 @@ def test_share_button_ships_visible_beside_new_chat() -> None:
     btn_block = html[btn.start() : html.find("</button>", btn.start())]
     assert '>Share</span>' in btn_block
     # Beside New chat (the Save pill is gone): after it, still inside
-    # .chat-shell, above #messages.
+    # .chat-shell — below #messages, above the composer (phase 65
+    # moved the row to the bottom of the column).
     shell_idx = html.find('class="container chat-shell"')
     new_idx = html.find('id="new-chat-btn"')
     messages_idx = html.find('id="messages"')
-    assert -1 < shell_idx < new_idx < btn.start() < messages_idx, (
-        "the button must sit beside #new-chat-btn in .chat-shell, above #messages"
+    messages_end = html.find("</section>", messages_idx)
+    composer_idx = html.find('<form class="composer" id="composer"')
+    assert -1 < shell_idx < new_idx < btn.start() < composer_idx, (
+        "the button must sit beside #new-chat-btn in .chat-shell, below "
+        "#messages, above the composer (phase 65)"
     )
+    assert messages_end < new_idx, ("the row moved below the #messages section")
     for other in (SOURCES_HTML, GIT_SOURCES_HTML, DOCUMENT_HTML, LOGIN_HTML,
                   TUNING_HTML, Path(FRONTEND / "history.html")):
         assert 'id="share-chat-btn"' not in other.read_text(encoding="utf-8"), (
@@ -673,13 +681,15 @@ def test_toast_css_top_right_brand_family_and_reduced_motion() -> None:
 
 
 def test_chat_actions_wrapper_holds_both_pills_in_order() -> None:
-    """index.html (task 05, A5): ONE ``<div class="chat-actions">``
-    wraps BOTH pills — its element children are exactly the two
-    buttons, in the A5 order New chat → Share. The wrapper replaces
-    the two pills as direct children of ``.chat-shell`` (a normal
-    column child): inside the shell, above ``#messages``; nothing else
-    lands between the steering announcer and the row, and nothing but
-    the phase-49 comment lands between the row and ``#messages``. No
+    """index.html (task 05, A5; phase 65 task 01): ONE
+    ``<div class="chat-actions">`` wraps BOTH pills — its element
+    children are exactly the two buttons, in the A5 order New chat →
+    Share. The wrapper is a normal ``.chat-shell`` column child, but
+    phase 65 (2026-09-01, ``TODO.md`` L3, owner confirmation) moved it
+    from the top of the column to the bottom: below the ``#messages``
+    section, directly above the composer; nothing but the row's own
+    comment lands between ``#messages`` and the row, and nothing but
+    the composer comment lands between the row and the composer. No
     other page carries ``.chat-actions`` (chat-page only, like the
     pills)."""
     html = _index()
@@ -694,23 +704,31 @@ def test_chat_actions_wrapper_holds_both_pills_in_order() -> None:
     new_i = wrap.find('id="new-chat-btn"')
     share_i = wrap.find('id="share-chat-btn"')
     assert -1 < new_i < share_i, "A5 order: New chat first, then Share"
-    # Position: a .chat-shell column child, above #messages — the
-    # kb-banner / stale-banner / steering / announcer structure is
-    # untouched (nothing else with an id around the row).
+    # Position: a .chat-shell column child, BELOW #messages and directly
+    # above the composer (phase 65 — the top of the column is now
+    # banner → steering → announcer → messages; nothing else with an id
+    # around the row).
     shell_idx = html.find('class="container chat-shell"')
     messages_idx = html.find('id="messages"')
-    assert -1 < shell_idx < start < end < messages_idx, (
-        "the row is a .chat-shell column child, above #messages"
-    )
-    ann_idx = html.find('id="steering-announcer"')
-    between = html[html.find("</p>", ann_idx):start]
-    assert "id=" not in between and "<button" not in between, (
-        "no other element lands between the announcer and the row"
-    )
-    after = html[end:messages_idx]
-    assert "id=" not in after and "<button" not in after, (
-        "nothing but the phase-49 comment lands between the row and #messages"
+    messages_end = html.find("</section>", messages_idx)
+    composer_idx = html.find('<form class="composer" id="composer"')
+    assert -1 < shell_idx < messages_end < start < end < composer_idx, (
+        "the row is a .chat-shell column child, below #messages, above the composer"
     )
+    between = html[messages_end:start]
+    assert (
+        "id=" not in between
+        and "<button" not in between
+        and "<section" not in between
+        and "<form" not in between
+    ), ("nothing but the row's comment lands between #messages and the row")
+    after = html[end:composer_idx]
+    assert (
+        "id=" not in after
+        and "<button" not in after
+        and "<section" not in after
+        and "<form" not in after
+    ), ("nothing but the composer comment lands between the row and the composer")
     for other in (SOURCES_HTML, GIT_SOURCES_HTML, DOCUMENT_HTML, LOGIN_HTML,
                   TUNING_HTML, Path(FRONTEND / "history.html")):
         assert "chat-actions" not in other.read_text(encoding="utf-8"), (