assistant2: Adjust spacing and icons on the context picker (#23607)

Just fine-tuning spacing, icon size and color, and ensure they're are
consistent throughout.

Release Notes:

- N/A

assets/icons/file.svg

@@ -1,8 +1,4 @@
-<svg width="15" height="15" viewBox="0 0 15 15" fill="none" xmlns="http://www.w3.org/2000/svg">
-  <path
-    fill-rule="evenodd"
-    clip-rule="evenodd"
-    d="M3.5 2C3.22386 2 3 2.22386 3 2.5V12.5C3 12.7761 3.22386 13 3.5 13H11.5C11.7761 13 12 12.7761 12 12.5V6H8.5C8.22386 6 8 5.77614 8 5.5V2H3.5ZM9 2.70711L11.2929 5H9V2.70711ZM2 2.5C2 1.67157 2.67157 1 3.5 1H8.5C8.63261 1 8.75979 1.05268 8.85355 1.14645L12.8536 5.14645C12.9473 5.24021 13 5.36739 13 5.5V12.5C13 13.3284 12.3284 14 11.5 14H3.5C2.67157 14 2 13.3284 2 12.5V2.5Z"
-    fill="currentColor"
-  />
+<svg width="16" height="16" viewBox="0 0 16 16" fill="none" xmlns="http://www.w3.org/2000/svg">
+<path d="M10.0001 1.33334H4.00008C3.64646 1.33334 3.30732 1.47382 3.05727 1.72387C2.80722 1.97392 2.66675 2.31305 2.66675 2.66668V13.3333C2.66675 13.687 2.80722 14.0261 3.05727 14.2762C3.30732 14.5262 3.64646 14.6667 4.00008 14.6667H12.0001C12.3537 14.6667 12.6928 14.5262 12.9429 14.2762C13.1929 14.0261 13.3334 13.687 13.3334 13.3333V4.66668L10.0001 1.33334Z" stroke="black" stroke-width="1.5" stroke-linecap="round" stroke-linejoin="round"/>
+<path d="M9.33325 1.33334V4.00001C9.33325 4.35363 9.47373 4.69277 9.72378 4.94282C9.97383 5.19287 10.313 5.33334 10.6666 5.33334H13.3333" stroke="black" stroke-width="1.5" stroke-linecap="round" stroke-linejoin="round"/>
 </svg>