new_dm: Add UI for starting new DM conversations

Add a modal bottom sheet UI for starting direct messages:
- Search and select users from global list
- Support single and group DMs
- Navigate to message list after selection

Design reference: https://www.figma.com/design/1JTNtYo9memgW7vV6d0ygq/Zulip-Mobile?node-id=4903-31879&p=f&t=pQP4QcxpccllCF7g-0
Fixes: #127

Author: chimnayajith

assets/l10n/app_en.arb

@@ -409,13 +409,9 @@
   "@composeBoxGenericContentHint": {
     "description": "Hint text for content input when sending a message."
   },
-  "newDmSheetBackButtonLabel": "Back",
-  "@newDmSheetBackButtonLabel": {
-    "description": "Label for the back button in the new DM sheet, allowing the user to return to the previous screen."
-  },
-  "newDmSheetNextButtonLabel": "Next",
-  "@newDmSheetNextButtonLabel": {
-    "description": "Label for the front button in the new DM sheet, if applicable, for navigation or action."
+  "newDmSheetComposeButtonLabel": "Compose",
+  "@newDmSheetComposeButtonLabel": {
+    "description": "Label for the compose button in the new DM sheet that starts composing a message to the selected users."
   },
   "newDmSheetScreenTitle": "New DM",
   "@newDmSheetScreenTitle": {
@@ -431,7 +427,7 @@
   },
   "newDmSheetSearchHintSomeSelected": "Add another user…",
   "@newDmSheetSearchHintSomeSelected": {
-    "description": "Hint text for the search bar when at least one user is selected"
+    "description": "Hint text for the search bar when at least one user is selected."
   },
   "newDmSheetNoUsersFound": "No users found",
   "@newDmSheetNoUsersFound": {

lib/generated/l10n/zulip_localizations.dart

@@ -691,17 +691,11 @@ abstract class ZulipLocalizations {
   /// **'Type a message'**
   String get composeBoxGenericContentHint;
 
-  /// Label for the back button in the new DM sheet, allowing the user to return to the previous screen.
+  /// Label for the compose button in the new DM sheet that starts composing a message to the selected users.
   ///
   /// In en, this message translates to:
-  /// **'Back'**
-  String get newDmSheetBackButtonLabel;
-
-  /// Label for the front button in the new DM sheet, if applicable, for navigation or action.
-  ///
-  /// In en, this message translates to:
-  /// **'Next'**
-  String get newDmSheetNextButtonLabel;
+  /// **'Compose'**
+  String get newDmSheetComposeButtonLabel;
 
   /// Title displayed at the top of the new DM screen.
   ///
@@ -721,7 +715,7 @@ abstract class ZulipLocalizations {
   /// **'Add one or more users'**
   String get newDmSheetSearchHintEmpty;
 
-  /// Hint text for the search bar when at least one user is selected
+  /// Hint text for the search bar when at least one user is selected.
   ///
   /// In en, this message translates to:
   /// **'Add another user…'**

lib/generated/l10n/zulip_localizations_ar.dart

@@ -344,10 +344,7 @@ class ZulipLocalizationsAr extends ZulipLocalizations {
   String get composeBoxGenericContentHint => 'Type a message';
 
   @override
-  String get newDmSheetBackButtonLabel => 'Back';
-
-  @override
-  String get newDmSheetNextButtonLabel => 'Next';
+  String get newDmSheetComposeButtonLabel => 'Compose';
 
   @override
   String get newDmSheetScreenTitle => 'New DM';

lib/generated/l10n/zulip_localizations_de.dart

@@ -344,10 +344,7 @@ class ZulipLocalizationsDe extends ZulipLocalizations {
   String get composeBoxGenericContentHint => 'Type a message';
 
   @override
-  String get newDmSheetBackButtonLabel => 'Back';
-
-  @override
-  String get newDmSheetNextButtonLabel => 'Next';
+  String get newDmSheetComposeButtonLabel => 'Compose';
 
   @override
   String get newDmSheetScreenTitle => 'New DM';

lib/generated/l10n/zulip_localizations_en.dart

@@ -344,10 +344,7 @@ class ZulipLocalizationsEn extends ZulipLocalizations {
   String get composeBoxGenericContentHint => 'Type a message';
 
   @override
-  String get newDmSheetBackButtonLabel => 'Back';
-
-  @override
-  String get newDmSheetNextButtonLabel => 'Next';
+  String get newDmSheetComposeButtonLabel => 'Compose';
 
   @override
   String get newDmSheetScreenTitle => 'New DM';

lib/generated/l10n/zulip_localizations_ja.dart

@@ -344,10 +344,7 @@ class ZulipLocalizationsJa extends ZulipLocalizations {
   String get composeBoxGenericContentHint => 'Type a message';
 
   @override
-  String get newDmSheetBackButtonLabel => 'Back';
-
-  @override
-  String get newDmSheetNextButtonLabel => 'Next';
+  String get newDmSheetComposeButtonLabel => 'Compose';
 
   @override
   String get newDmSheetScreenTitle => 'New DM';

lib/generated/l10n/zulip_localizations_nb.dart

@@ -344,10 +344,7 @@ class ZulipLocalizationsNb extends ZulipLocalizations {
   String get composeBoxGenericContentHint => 'Type a message';
 
   @override
-  String get newDmSheetBackButtonLabel => 'Back';
-
-  @override
-  String get newDmSheetNextButtonLabel => 'Next';
+  String get newDmSheetComposeButtonLabel => 'Compose';
 
   @override
   String get newDmSheetScreenTitle => 'New DM';

lib/generated/l10n/zulip_localizations_pl.dart

@@ -351,10 +351,7 @@ class ZulipLocalizationsPl extends ZulipLocalizations {
   String get composeBoxGenericContentHint => 'Wpisz wiadomość';
 
   @override
-  String get newDmSheetBackButtonLabel => 'Back';
-
-  @override
-  String get newDmSheetNextButtonLabel => 'Next';
+  String get newDmSheetComposeButtonLabel => 'Compose';
 
   @override
   String get newDmSheetScreenTitle => 'New DM';

lib/generated/l10n/zulip_localizations_ru.dart

@@ -352,10 +352,7 @@ class ZulipLocalizationsRu extends ZulipLocalizations {
   String get composeBoxGenericContentHint => 'Ввести сообщение';
 
   @override
-  String get newDmSheetBackButtonLabel => 'Back';
-
-  @override
-  String get newDmSheetNextButtonLabel => 'Next';
+  String get newDmSheetComposeButtonLabel => 'Compose';
 
   @override
   String get newDmSheetScreenTitle => 'New DM';

lib/generated/l10n/zulip_localizations_sk.dart

@@ -344,10 +344,7 @@ class ZulipLocalizationsSk extends ZulipLocalizations {
   String get composeBoxGenericContentHint => 'Type a message';
 
   @override
-  String get newDmSheetBackButtonLabel => 'Back';
-
-  @override
-  String get newDmSheetNextButtonLabel => 'Next';
+  String get newDmSheetComposeButtonLabel => 'Compose';
 
   @override
   String get newDmSheetScreenTitle => 'New DM';

lib/generated/l10n/zulip_localizations_uk.dart

@@ -353,10 +353,7 @@ class ZulipLocalizationsUk extends ZulipLocalizations {
   String get composeBoxGenericContentHint => 'Ввести повідомлення';
 
   @override
-  String get newDmSheetBackButtonLabel => 'Back';
-
-  @override
-  String get newDmSheetNextButtonLabel => 'Next';
+  String get newDmSheetComposeButtonLabel => 'Compose';
 
   @override
   String get newDmSheetScreenTitle => 'New DM';

lib/generated/l10n/zulip_localizations_zh.dart

@@ -344,10 +344,7 @@ class ZulipLocalizationsZh extends ZulipLocalizations {
   String get composeBoxGenericContentHint => 'Type a message';
 
   @override
-  String get newDmSheetBackButtonLabel => 'Back';
-
-  @override
-  String get newDmSheetNextButtonLabel => 'Next';
+  String get newDmSheetComposeButtonLabel => 'Compose';
 
   @override
   String get newDmSheetScreenTitle => 'New DM';

lib/model/autocomplete.dart

@@ -556,7 +556,6 @@ class MentionAutocompleteView extends AutocompleteView<MentionAutocompleteQuery,
   /// returns a positive number if [userB] is more recent than [userA],
   /// and returns `0` if both [userA] and [userB] are equally recent
   /// or there is no DM exchanged with them whatsoever.
-  @visibleForTesting
   static int compareByDms(User userA, User userB, {required PerAccountStore store}) {
     final recentDms = store.recentDmConversationsView;
     final aLatestMessageId = recentDms.latestMessagesByRecipient[userA.userId];