refactor: rename to common/, clients/desktop, clients/wearos

Move three directories into their target topology:
- doctate-common/ -> common/
- client-desktop/ -> clients/desktop/
- watch/wearos/   -> clients/wearos/

Update doctate-common path-dependency in 3 Cargo.toml files
(server, clients/desktop, experiments) and the workspace
members list in the root Cargo.toml. Crate names unchanged
(doctate-server, doctate-common, doctate-desktop).

Workspace still in single-Cargo.lock form; isolation into
standalone workspaces follows in stage 3. All 508 tests pass,
experiments standalone-workspace also resolves the new path.

common/src/url.rs

@@ -0,0 +1,55 @@
+//! Small URL-assembly helpers shared by every HTTP caller in the
+//! workspace.
+//!
+//! All clients (desktop, server-internal, server-to-Ollama/Whisper)
+//! end up building `{base_url}{path}` where `base_url` comes from
+//! config and may or may not carry a trailing slash. The raw
+//! `format!("{}{}", base.trim_end_matches('/'), path)` pattern was
+//! duplicated in seven call sites; centralizing it here keeps any
+//! future rule (enforce a leading slash on the path, tolerate
+//! `http://host/` with a path segment, normalize percent-encoding)
+//! in one place.
+
+/// Join a base URL with an absolute path, normalizing any trailing
+/// slash on the base. The path is expected to start with `/`; no
+/// validation is performed — callers already pass constants like
+/// [`crate::UPLOAD_PATH`].
+///
+/// Examples:
+/// - `join_url("http://h", "/a")` → `"http://h/a"`
+/// - `join_url("http://h/", "/a")` → `"http://h/a"`
+/// - `join_url("http://h//", "/a")` → `"http://h/a"`
+pub fn join_url(base: &str, path: &str) -> String {
+    let mut out = String::with_capacity(base.len() + path.len());
+    out.push_str(base.trim_end_matches('/'));
+    out.push_str(path);
+    out
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn no_trailing_slash_on_base() {
+        assert_eq!(join_url("http://h", "/a"), "http://h/a");
+    }
+
+    #[test]
+    fn single_trailing_slash_on_base() {
+        assert_eq!(join_url("http://h/", "/a"), "http://h/a");
+    }
+
+    #[test]
+    fn multiple_trailing_slashes_on_base() {
+        assert_eq!(join_url("http://h///", "/a"), "http://h/a");
+    }
+
+    #[test]
+    fn nested_path() {
+        assert_eq!(
+            join_url("https://example.com/", "/api/upload"),
+            "https://example.com/api/upload"
+        );
+    }
+}