Add Projects: third tab, swipe-to-file, per-project note capture

Notes gain an optional project (schema v4, additive). Projects derive
from note values like tags — no separate entity. Tab naming
(Projects/Categories) is a Settings choice applied across the UI.

Claude-Session: https://claude.ai/code/session_014esDWi42URLEC6Cj17hGQ3

Notes/Storage/SyncEngine.swift

@@ -136,9 +136,10 @@ final class SyncEngine {
         text: String,
         source: Note.Source = .typed,
         tags: [String] = [],
-        context: CaptureContext
+        context: CaptureContext,
+        project: String? = nil
     ) async throws -> Note {
-        let note = Note.create(text: text, source: source, tags: tags, context: context)
+        let note = Note.create(text: text, source: source, tags: tags, context: context, project: project)
         try await save(note)
         return note
     }
@@ -202,7 +203,8 @@ final class SyncEngine {
         text: String = "",
         tags: [String] = [],
         context: CaptureContext,
-        transcriberDeviceID: String
+        transcriberDeviceID: String,
+        project: String? = nil
     ) async throws -> Note {
         guard let store else {
             report("Note not saved — iCloud not connected")
@@ -215,7 +217,7 @@ final class SyncEngine {
             transcriptionLocaleID: nil,
             transcribedAt: nil
         )
-        let note = Note.create(text: text, source: .transcribed, tags: tags, context: context, audio: audio)
+        let note = Note.create(text: text, source: .transcribed, tags: tags, context: context, audio: audio, project: project)
         do {
             let audioData = try Data(contentsOf: audioFileURL)
             try await store.writeData(audioData, to: Self.dataPath(Note.audioRelativePath(forID: note.id)))
@@ -322,6 +324,20 @@ final class SyncEngine {
         try await updateNote(note)
     }
 
+    // MARK: - Organization
+
+    /// Assign a note to a project (or clear it with nil). Re-reads the file —
+    /// the authority — so a concurrent edit isn't clobbered; the cache catches
+    /// up via the monitor as usual.
+    func assignProject(id: ULID, project: String?) async throws {
+        guard let store else { throw SyncError.iCloudUnavailable }
+        guard let raw = try? await store.read(Note.self, from: Self.dataPath(Note.relativePath(forID: id))),
+              raw.isReadable else { return }
+        var note = migrateIfNeeded(raw)
+        note.payload.project = project
+        try await updateNote(note)
+    }
+
     // MARK: - Watch ingestion
 
     /// Local directory where the phone receiver (`PhoneWatchReceiver`, a later
@@ -763,6 +779,8 @@ final class SyncEngine {
     /// the transcript merged with user typing — indistinguishable by then) in
     /// `text`; move that whole text into the first attempt so the v3 invariant
     /// "text is user writing only" holds. Confidence was never recorded ⇒ nil.
+    /// v3 → v4 is additive-only (new optional `payload.project`), so no
+    /// migration action is needed beyond the version stamp.
     /// Internal (not private) so the migration policy is unit-testable.
     func migrateIfNeeded(_ note: Note) -> Note {
         guard note.meta.schemaVersion < Note.currentSchemaVersion else { return note }