Replace the compose FAB with a Liquid Glass compose pill in the bottom bar

## Summary

- Remove the compose FAB, the new chat FAB, the "load latest" button and the
  Discover/Following inline composer prompt. The new chat entry point still
  needs a replacement.
- Add `features/composePrompt`: screens register a pill config (label,
  accessibility text, an `open` callback) and the bottom bar renders a single
  pill driven by that context. Registration follows the screen's presence, so
  the pill fades in and out with pushes, pops and swipe-back, and the label
  switches to whichever screen is most present mid-transition. The bar's top
  border hides while a pill is registered.
- The pill is a Liquid Glass view with `isInteractive`, toggling its glass
  style with the system animation as it comes and goes, with a gradient behind
  it that fades further than the thread version so content shows through the
  glass. It includes the camera and gallery buttons from the old feed prompt.
- When the bottom bar hides, the pill drops into the bar's space and scales
  down, inset equally from the left, right and bottom edges so its corners sit
  concentric with the device bevels; while the bar shows it hugs the edges.
- Home, Notifications, Feeds, custom feeds and lists open the composer; a
  profile pre-fills a mention as the FAB did; a thread opens the reply
  composer, including media picked from the pill.

## Test plan

- [ ] Home: pill above the bar; tap opens composer; camera/gallery open with media
- [ ] Home: scroll down hides the bar and the pill drops, shrinks and sits inset from the bevels; scroll up restores it
- [ ] Push a thread from Home: label crossfades to "Write your reply" mid-transition; tap opens the reply composer
- [ ] Thread with replies disabled: pill fades out on push and back in on pop
- [ ] Profile of another user: composer opens with their handle
- [ ] Search tab / Messages tab: pill fades out; pill fades back when returning
- [ ] Conversation screen: pill fades out while the bar slides away
- [ ] Android / iOS < 26: plain pill fallback fades in and out
- [ ] Mobile web: pill shows above the web bottom bar

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01QoggCVt9XgpKbjrTZjoJD9

__e2e__/flows/composer-self-label.yml

@@ -14,9 +14,9 @@ appId: xyz.blueskyweb.app
 
 # Post an image with the porn label
 - assertVisible:
-    id: "composeFAB"
+    id: "composePromptPill"
 - tapOn:
-    id: "composeFAB"
+    id: "composePromptPill"
 - inputText: "Post with an image"
 - tapOn:
     id: "openMediaBtn"

__e2e__/flows/composer.yml

@@ -13,16 +13,16 @@ appId: xyz.blueskyweb.app
       id: "viewHeaderHomeFeedPrefsBtn"
 
 - assertVisible:
-    id: "composeFAB"
+    id: "composePromptPill"
 - tapOn:
-    id: "composeFAB"
+    id: "composePromptPill"
 - inputText: "Post text only"
 - tapOn:
     id: "composerPublishBtn"
 - assertVisible:
-    id: "composeFAB"
+    id: "composePromptPill"
 - tapOn:
-    id: "composeFAB"
+    id: "composePromptPill"
 - inputText: "Post with an image"
 - tapOn:
     id: "openMediaBtn"
@@ -32,14 +32,14 @@ appId: xyz.blueskyweb.app
 - tapOn:
     id: "composerPublishBtn"
 - assertVisible:
-    id: "composeFAB"
+    id: "composePromptPill"
 - tapOn:
-    id: "composeFAB"
+    id: "composePromptPill"
 - inputText: "Post with a https://example.com link card"
 - tapOn:
     id: "composerPublishBtn"
 - assertVisible:
-    id: "composeFAB"
+    id: "composePromptPill"
 - tapOn:
     id: "e2eRefreshHome"
 - tapOn:
@@ -54,7 +54,7 @@ appId: xyz.blueskyweb.app
 - tapOn:
     id: "composerPublishBtn"
 - assertVisible:
-    id: "composeFAB"
+    id: "composePromptPill"
 - tapOn:
     id: "replyBtn"
 # Wait for the composer to fully open before typing.
@@ -71,7 +71,7 @@ appId: xyz.blueskyweb.app
 - tapOn:
     id: "composerPublishBtn"
 - assertVisible:
-    id: "composeFAB"
+    id: "composePromptPill"
 - tapOn:
     id: "replyBtn"
 # Wait for the composer to fully open before typing.
@@ -83,7 +83,7 @@ appId: xyz.blueskyweb.app
 - tapOn:
     id: "composerPublishBtn"
 - assertVisible:
-    id: "composeFAB"
+    id: "composePromptPill"
 - tapOn:
     id: "repostBtn"
 - tapOn:
@@ -92,7 +92,7 @@ appId: xyz.blueskyweb.app
 - tapOn:
     id: "composerPublishBtn"
 - assertVisible:
-    id: "composeFAB"
+    id: "composePromptPill"
 - tapOn:
     id: "repostBtn"
 - tapOn:
@@ -106,7 +106,7 @@ appId: xyz.blueskyweb.app
 - tapOn:
     id: "composerPublishBtn"
 - assertVisible:
-    id: "composeFAB"
+    id: "composePromptPill"
 - tapOn:
     id: "repostBtn"
 - tapOn:
@@ -115,4 +115,4 @@ appId: xyz.blueskyweb.app
 - tapOn:
     id: "composerPublishBtn"
 - assertVisible:
-    id: "composeFAB"
+    id: "composePromptPill"

__e2e__/flows/thread-muting.yml

@@ -14,9 +14,9 @@ appId: xyz.blueskyweb.app
     visible:
       id: "viewHeaderHomeFeedPrefsBtn"
 - assertVisible:
-    id: "composeFAB"
+    id: "composePromptPill"
 - tapOn:
-    id: "composeFAB"
+    id: "composePromptPill"
 - inputText: "Test thread"
 - tapOn:
     id: "composerPublishBtn"
@@ -24,7 +24,7 @@ appId: xyz.blueskyweb.app
 # out. Without a settle guard the next action can race the closing composer.
 - extendedWaitUntil:
     visible:
-      id: "composeFAB"
+      id: "composePromptPill"
     timeout: 10000
 
 # Login, reply to the thread, and log out
@@ -48,7 +48,7 @@ appId: xyz.blueskyweb.app
 # Wait for the composer to close before signing out.
 - extendedWaitUntil:
     visible:
-      id: "composeFAB"
+      id: "composePromptPill"
     timeout: 10000
 
 # Login, confirm notification exists, mute thread, and log out