[AI Assistance] Fix icons getting cut off on small screens

Matches the behaviour of other panels under small widths.

Bug: none
Change-Id: I82c6dcac5e235d6ced3320891c42640b83aa308c
Reviewed-on: https://chromium-review.googlesource.com/c/devtools/devtools-frontend/+/7206121
Auto-Submit: Nikolay Vitkov <nvitkov@chromium.org>
Commit-Queue: Nikolay Vitkov <nvitkov@chromium.org>
Commit-Queue: Alex Rudenko <alexrudenko@chromium.org>
Reviewed-by: Alex Rudenko <alexrudenko@chromium.org>

Author: Lightning00Blade

front_end/panels/ai_assistance/aiAssistancePanel.css

@@ -6,6 +6,7 @@
 
 .toolbar-container {
   display: flex;
+  flex-wrap: wrap;
   background-color: var(--sys-color-cdt-base-container);
   border-bottom: 1px solid var(--sys-color-divider);
   flex: 0 0 auto;