fix(custom-model): pass context limits and selected model to CLIs, and add model picker filter

- opencode: write limit.context/output from the discovered context length (#749)
- codex: override the native launch model when a custom endpoint is selected (#750), and set model_context_window
- model picker: add a search/filter box with a no-matches line

src/web/public/index.html

@@ -1033,6 +1033,14 @@
         </div>
         <div class="modal-body">
           <p class="form-hint" id="customModelPickHint"></p>
+          <!-- Case-insensitive filter over the rendered rows (app.filterCustomModelPick):
+               a display layer only, the rows themselves are never re-rendered. Reset and
+               focused on every open, same in-memory rule as the rail's search box. -->
+          <input type="search" id="customModelPickSearch" class="session-sidebar-filter-input custom-model-pick-search"
+            placeholder="Search models" aria-label="Search models"
+            autocomplete="off" autocapitalize="off" spellcheck="false" enterkeyhint="search"
+            oninput="app.filterCustomModelPick(this.value)">
+          <p class="form-hint custom-model-pick-no-matches" id="customModelPickNoMatches" role="status" hidden>No models match</p>
           <div id="customModelPickList" class="run-mode-custom-models"></div>
         </div>
       </div>

src/web/public/session-ui.js

@@ -1088,13 +1088,53 @@ Object.assign(CodemanApp.prototype, {
         const promotion = m === currentlyLoaded ? 'Currently loaded' : m === lastUsed ? 'Last used' : null;
         const tags = [promotion, m === host.defaultModelId ? 'Default' : null].filter(Boolean);
         const arg = escapeHtml(JSON.stringify(m));
+        // data-model-id is the filter's haystack (escapeHtml covers `"` as well as
+        // `<>&`, so a hostile model id cannot break out of the attribute); the
+        // filter reads it back through dataset, which decodes it.
         return `
-          <button class="run-mode-option" onclick="app.chooseCustomModelAndRun(${arg})">
+          <button class="run-mode-option" data-model-id="${escapeHtml(m)}" onclick="app.chooseCustomModelAndRun(${arg})">
             <span class="run-mode-dot ${escapeHtml(mode)}"></span>${escapeHtml(m)}${tags.map((t) => ` <span class="set-scope">${escapeHtml(t)}</span>`).join('')}
           </button>`;
       })
       .join('');
     modal.classList.add('active');
+    // A fresh open always starts unfiltered with the caret in the search box — the
+    // list was just rebuilt, so clearing the input is the whole reset; focus is the
+    // user's next keystroke away. Inside the generation guard above, so a
+    // superseded probe can neither focus nor clear a modal that now shows another
+    // endpoint's models.
+    const search = document.getElementById('customModelPickSearch');
+    if (search) {
+      search.value = '';
+      search.focus();
+    }
+    this.filterCustomModelPick('');
+  },
+
+  /**
+   * View filter for the open "Choose a model" picker: case-insensitive substring
+   * over each row's model id, driven from the search input's own `oninput`.
+   * Deliberately toggles `hidden` on the already-rendered buttons rather than
+   * re-rendering from a second copy of the model list: the loaded/last-used
+   * promotion, the Default pill, the escaped inline click argument and the async
+   * generation guard all then stay exactly where they are, and clearing the
+   * query restores the list byte for byte. ⚠️ `.run-mode-option` carries its own
+   * `display: flex` (styles.css, restated in mobile.css), which outranks the UA
+   * `[hidden]` rule, so styles.css re-asserts `display: none !important` for
+   * these rows — without it the filter would silently do nothing.
+   */
+  filterCustomModelPick(value) {
+    const list = document.getElementById('customModelPickList');
+    if (!list) return;
+    const query = String(value || '').trim().toLowerCase();
+    let visible = 0;
+    for (const btn of list.querySelectorAll('button[data-model-id]')) {
+      const match = !query || btn.dataset.modelId.toLowerCase().includes(query);
+      btn.hidden = !match;
+      if (match) visible += 1;
+    }
+    const noMatches = document.getElementById('customModelPickNoMatches');
+    if (noMatches) noMatches.hidden = visible > 0;
   },
 
   closeCustomModelPickModal() {

src/web/public/styles.css

@@ -7807,6 +7807,27 @@ html[data-skin="og"] .welcome-primary:hover {
   opacity: 0.8;
 }
 
+/* The picker's search box reuses .session-sidebar-filter-input's theme-token
+   styling (same reasoning as the .set-scope pill above) — only its own spacing
+   and the no-matches line are added here. */
+#customModelPickModal .custom-model-pick-search {
+  margin-bottom: 0.5rem;
+}
+
+#customModelPickModal .custom-model-pick-no-matches {
+  text-align: center;
+  padding: 1rem 0;
+}
+
+/* A filtered-out row's `hidden` must actually hide it: `.run-mode-option` sets
+   `display: flex` (and mobile.css restates the class in a media query), which
+   outranks the UA `[hidden] { display: none }` rule, so the filter would
+   silently do nothing without this re-assertion. Scoped to this modal's rows;
+   the Run menu's own .run-mode-option entries never take `hidden`. */
+#customModelPickModal .run-mode-option[hidden] {
+  display: none !important;
+}
+
 /* Custom Model Endpoint Profiles: llama-swap model-swap confirmation — replaces a native
    confirm() popup (docs/custom-model-endpoints-plan.md) so it looks and feels like the
    rest of the app instead of a browser chrome dialog. Shares the context-window-too-small