Initial commit: standalone quiz-testing system

Full-stack F# (Domain/Server/Client via Fable+Elmish+Feliz), PostgreSQL
persistence via Dapper, Docker Compose deployment. Student quiz-taking flow
with time-limit enforcement and focus-loss tracking, Teacher question bank
and quiz builder with results analytics, Admin user management.

src/Client/Features/Teacher/Home/State.fs

@@ -0,0 +1,50 @@
+module Client.Features.Teacher.Home.State
+
+open Elmish
+open Domain
+open Client.Features
+open Client.Features.Teacher.Home.Types
+
+/// `role` decides whether the Admin-only "Пользователи" tab is shown/loaded —
+/// Teacher and Admin otherwise share this exact same page (see DESIGN.md §2:
+/// Admin = Teacher + user management).
+let init (role: Role) : Model * Cmd<Msg> =
+    let questionsModel, questionsCmd = Teacher.Questions.State.init ()
+    let testsModel, testsCmd = Teacher.Tests.State.init ()
+
+    let usersCmd =
+        match role with
+        | Admin -> Cmd.map UsersMsg (Cmd.ofMsg Admin.Users.Types.LoadUsers)
+        | Teacher
+        | Student -> Cmd.none
+
+    { Tab = QuestionsTab
+      Role = role
+      Questions = questionsModel
+      Tests = testsModel
+      Users = Admin.Users.Types.empty },
+    Cmd.batch [ Cmd.map QuestionsMsg questionsCmd; Cmd.map TestsMsg testsCmd; usersCmd ]
+
+let update (token: string option) (msg: Msg) (model: Model) : Model * Cmd<Msg> =
+    match msg with
+    | SwitchTab tab -> { model with Tab = tab }, Cmd.none
+    | QuestionsMsg(Teacher.Questions.Types.TopicCreated topic as subMsg) ->
+        let m, cmd = Teacher.Questions.State.update token subMsg model.Questions
+
+        { model with
+            Questions = m
+            // Questions and Tests keep independent `Topics` lists (own VSA
+            // slices, own `LoadTopics` on init) — a topic created in one
+            // must be mirrored into the other, or the quiz question-picker
+            // never sees topics added after the page first loaded.
+            Tests = { model.Tests with Topics = model.Tests.Topics @ [ topic ] } },
+        Cmd.map QuestionsMsg cmd
+    | QuestionsMsg subMsg ->
+        let m, cmd = Teacher.Questions.State.update token subMsg model.Questions
+        { model with Questions = m }, Cmd.map QuestionsMsg cmd
+    | TestsMsg subMsg ->
+        let m, cmd = Teacher.Tests.State.update token subMsg model.Tests
+        { model with Tests = m }, Cmd.map TestsMsg cmd
+    | UsersMsg subMsg ->
+        let m, cmd = Admin.Users.State.update token subMsg model.Users
+        { model with Users = m }, Cmd.map UsersMsg cmd