feat: retain live page mounts and update shared UI references across aliases

src/api.rs

@@ -584,10 +584,10 @@ Send PUT bodies as `text/plain; charset=utf-8`.
 `POST http://{address}/v1/namespaces/{name}/repl` accepts statements, function
  definitions and expressions as text/plain. Consecutive requests use one real VM
 and globals dictionary on the execution worker. `title = ui.text("Hello")` creates
-an object without displaying it. A later `page.render(root)` publishes its page.
+an object without displaying it. A later `page.render(root)` mounts its page. UI references share replacement state: after mounting, assigning a new UI value to a reference updates its aliases and mounted positions. `page.unmount()` releases the mount.
 `let title = ...` is also supported. `_` retains the actual last value. No input
 history is replayed. Responses include session/input IDs, value, binding count,
-rendered flag and revision. Without render the displayed page/revision stay unchanged.
+rendered flag and revision. Before the first mount the page/revision stay unchanged; afterwards successful inputs publish changed mounted references automatically.
 
 `DELETE http://{address}/v1/namespaces/{name}/repl` resets Console objects and bindings,
 leaving the displayed native snapshot intact. Parsing/compilation happen before
@@ -595,7 +595,7 @@ execution. On runtime error earlier statements in that input may remain live, bu
 its pending render is discarded; previous displayed page is preserved.
 
 Session limits: 256 executed inputs, 1 MiB transcript, 10000 cumulative AST nodes,
-4096 UI nodes and 64 pages. Reset to reclaim them. No VM handles cross to the window.
+4096 retained UI nodes and 64 retained pages. Unused slots are reclaimed between inputs; reset releases the session. No VM handles cross to the window.
 A newer accepted complete-source PUT or code DELETE invalidates queued Console
 inputs and resets the live context. They retain their existing snapshot semantics.
 GET /code returns the source of the displayed snapshot: exact submitted source for
@@ -616,7 +616,7 @@ Positional arguments only:
 - `ui.rect(width, height, radius = 0, color = "#DCE8FF")`.
 - `ui.column(padding, gap, child...)` and `ui.row(padding, gap, child...)`.
 - `ui.spacer(size)`.
-- `ui.page()` creates a page; `page.render(root)` sets its root. The last render
+- `ui.page()` creates a page; `page.render(root)` mounts its root; `page.unmount()` releases the mount. The last render
   in a successful submission selects the page shown in this namespace.
 
 Defaults above describe the host API; do not write keyword arguments in Endor.