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

frontend/assets/styles.css

@@ -423,17 +423,31 @@ html::after {
    (a normal .chat-shell column child). As a flex ITEM of the column it
    spans the column width, but as a flex ROW with align-items: center
    (not the column default stretch) each pill keeps its INTRINSIC
-   content width — two pills side by side, left-aligned in the column,
-   on desktop. The ≤640px block flips this to a vertical stack
-   (flex-direction: column + align-items: stretch — full-width pills,
-   New chat above Share; the existing ≤640px pill rules apply to the
-   stacked pills unchanged). The reading-column contract is untouched
-   (--chat-column: 46rem base, 92rem at >=1500px — PLAN §7 lineage).
-   */
+   content width — two pills side by side on desktop. The ≤640px block
+   flips this to a vertical stack (flex-direction: column +
+   align-items: stretch — full-width pills, New chat above Share; the
+   existing ≤640px pill rules apply to the stacked pills unchanged).
+   The reading-column contract is untouched (--chat-column: 46rem base,
+   92rem at >=1500px — PLAN §7 lineage).
+
+   Phase 65 (task 03, 2026-09-01, `TODO.md` L3, owner-locked A2): the
+   row is the TOP member of the pinned .chat-bottom cluster (task
+   01/02) and hugs the column's RIGHT edge on desktop
+   (justify-content: flex-end) — mirroring the right-aligned
+   "Save as doc" action of every brain bubble above it, so the
+   bottom-right of the chat reads as ONE aligned action column. The
+   pills keep their intrinsic widths (align-items: center already
+   beats the column default stretch; justify-content only shifts the
+   group). The vertical row↔composer spacing is the .chat-bottom
+   wrapper's 0.5rem gap (task 02). The ≤640px stack rule below is
+   UNCHANGED — with stretched full-width pills the horizontal
+   alignment is moot (the stacked pills already edge-to-edge the
+   column). */
 .chat-actions {
   display: flex;
   flex-direction: row;
   align-items: center;
+  justify-content: flex-end;
   gap: 0.6rem;
 }
 
@@ -1222,7 +1236,37 @@ details.thinking .thinking-text ul { margin: 0 0 0.5rem; }
    so messages scrolling behind the pinned box never show through it,
    and no z-index is added: DOM order already paints the composer over
    `.messages`, it never overlaps the sticky header (z 20) and stays
-   under the z-1000 document modal. */
+   under the z-1000 document modal.
+   Phase 65 (2026-09-01, `TODO.md` L3, owner-locked A1): the pin now
+   belongs to the .chat-bottom wrapper (rule below) — the row + this
+   form are ONE sticky unit; this composer's own sticky declaration is
+   kept, redundant inside the wrapper but pinned as a computed style by
+   tests/e2e/test_pinned_composer.py. */
+/* Phase 65 (owner-locked A1, 2026-09-01, `TODO.md` L3): the pinned
+   bottom cluster — the .chat-actions row + the #composer form as ONE
+   sticky unit (A1): the pills are literally always at the bottom of
+   the screen, even while the reader is scrolled up through a long
+   conversation (the rejected in-flow alternative would scroll away).
+   The sticky range is the .chat-shell containing block (the wrapper's
+   parent) — the same range the composer used to have alone — and the
+   .messages flex-grow still rests the WHOLE unit at the screen bottom
+   on short chats (the wrapper is the last shell child, so the grow
+   pushes it down). The shell's 1rem gap applies only ABOVE the unit,
+   from .messages — the 0.5rem gap here is the row↔composer spacing
+   INSIDE it. No z-index: the phase-12 sticky header (z 20) and the
+   phase-46 dropdown always stay on top, and at the document bottom the
+   unit settles back into flow above the footer (the composer's opaque
+   surface keeps messages hidden where the box overlaps them). The
+   composer's own sticky rule below stays — redundant here (its
+   containing block is the wrapper, so it cannot shift within the
+   unit), pinned by tests/e2e/test_pinned_composer.py. */
+.chat-bottom {
+  display: flex;
+  flex-direction: column;
+  gap: 0.5rem;
+  position: sticky;
+  bottom: env(safe-area-inset-bottom, 0);
+}
 .composer {
   display: flex;
   align-items: flex-end;