Chats system model - Chat tabs are visually inconsistent with the tabs in the right pane

### Description

The look and feel of the tabs in the Session chats is different from the one in the right pane. The tabs should align with the design system guidance and be consistent across the two.

### Issue Details

Item|Value
---|---
Issue Category|Bug
Target|Agents Window
VS Code Version|Code - Insiders 1.129.0-insider (Universal) (e8a3eada3426fa6848c7494ebe2291702fef4a61, 2026-07-10T19:51:00Z)
OS Version|Darwin arm64 25.5.0

System Info

Item|Value
---|---
VS Code Version|Code - Insiders 1.129.0-insider (Universal) (e8a3eada3426fa6848c7494ebe2291702fef4a61, 2026-07-10T19:51:00Z)
OS Version|Darwin arm64 25.5.0
CPUs|Apple M3 Pro (12 x 2400)
GPU Status|2d_canvas: enabled
GPU0: VENDOR= 0x106b [Google Inc. (Apple)], DEVICE=0x0000 [ANGLE (Apple, ANGLE Metal Renderer: Apple M3 Pro, Version 26.5.2 (Build 25F84))], DRIVER_VENDOR=Apple, DRIVER_VERSION=26.5.2 *ACTIVE*
Machine model name: Mac
Machine model version: 15.7
direct_rendering_display_compositor: disabled_off_ok
gpu_compositing: enabled
multiple_raster_threads: enabled_on
opengl: enabled_on
rasterization: enabled
raw_draw: disabled_off_ok
skia_graphite: enabled_on
trees_in_viz: disabled_off
video_decode: enabled
video_encode: enabled
webgl: enabled
webgpu: enabled
webnn: disabled_off
Load (avg)|4, 3, 4
Memory (System)|18.00GB (0.21GB free)
Process Argv|--crash-reporter-id b5a95500-3215-48c0-b59b-c1fa4f61cff6
Screen Reader|no
VM|0%
User Agent|Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_7) AppleWebKit/537.36 (KHTML, like Gecko) Code-Insiders/1.129.0-insider Chrome/148.0.7778.271 Electron/42.5.0 Safari/537.36
Installation pure|true

### Attachments