Unable to connect to tunnel after updating service remotely

### Description

1. Connected to remote tunnel from this client
2. Received pop-up asking to update Remote Tunnel Service
3. Chose "Update"
4. Got disconnected from tunnel
5. Noticed that VSCode client has update, so clicked on "Update"
6. Waited for restart
7. After restart, client started connecting automatically to tunnel but failed
8. Disconnected from tunnel manually
9. Tried to reconnect to tunnel, still failed
10. The client on the remote side says that the tunnel is open

### Issue Details

Item|Value
---|---
Issue Category|Bug
Target|Visual Studio Code - Insiders
VS Code Version|Code - Insiders 1.128.0-insider (2be9624b801009a53db8f629bd7762137d100007, 2026-07-02T16:57:42Z)
OS Version|Windows_NT arm64 10.0.29617

System Info

Item|Value
---|---
VS Code Version|Code - Insiders 1.128.0-insider (2be9624b801009a53db8f629bd7762137d100007, 2026-07-02T16:57:42Z)
OS Version|Windows_NT arm64 10.0.29617
CPUs|Snapdragon(R) X 12-core X1E80100 @ 3.40 GHz (12 x 2976)
GPU Status|2d_canvas: enabled
GPU0: VENDOR= 0x4d4f4351, DEVICE=0x36334330 [Qualcomm(R) Adreno(TM) X1-85 GPU], DRIVER_VENDOR=Qualcomm, DRIVER_VERSION=31.0.133.1 *ACTIVE*
GPU1: VENDOR= 0x1414, DEVICE=0x008c [Microsoft Basic Render Driver], DRIVER_VERSION=10.0.29617.1000
Machine model name:
Machine model version:
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: disabled_off
trees_in_viz: disabled_off
video_decode: enabled
video_encode: enabled
webgl: enabled
webgpu: enabled
webnn: disabled_off
Load (avg)|
Memory (System)|31.57GB (7.84GB free)
Process Argv|--crash-reporter-id 483f0690-a42a-46e0-ac71-0633f1ed0fe1
Screen Reader|no
VM|0%
Remote Error|Connection to 'cpc-kmere-6kgz3' could not be established WebSocket close with status code 1006
User Agent|Mozilla/5.0 (Windows NT 10.0) AppleWebKit/537.36 (KHTML, like Gecko) Code-Insiders/1.128.0-insider Chrome/148.0.7778.271 Electron/42.5.0 Safari/537.36
Installation pure|true

### Extensions

Extensions: none

A/B Experiments

```
vsliv368cf:30146710
pythonvspyt551:31249597
nativeloc1:31118317
dwcopilot:31158714
dwoutputs:31242946
copilot_t_ci:31333650
g012b348:31231168
pythonrdcb7:31268811
pythonpcpt1cf:31399617
6518g693:31302842
6abeh943:31336334
envsactivate1:31349248
editstats-enabled:31346256
cloudbuttont:31366566
3efgi100_wstrepl:31403338
metis_rerank_treatment1:31411021
cp_cls_t_966_ss:31526232
4je02754:31455664
c3h7c220:31478652
ge8j1254_inline_auto_hint_haiku:31490507
cp_cls_c_1081:31454833
conptydll_true:31485575
ia-use-proxy-models-svc:31446143
e9c30283:31453065
test_treatment2:31471001
c9b86496:31447327
idci7584:31454084
e3e4d672:31454087
ei9d7968:31462942
7e884298:31462391
7e187181:31482583
h08i8180_copy:31475366
ddid_t:31478204
hmra_i5g22:-9
bjc72774_agent_sandbox:31538428
7df3h592:31491241
cp_cls_t_1082:31535311
logging_enabled_new:31490725
jb_cp_cls_t_632:31543129
32d76977:31503652
ha629193:31508444
cdk-lw-on:31524445
f9bf7985:31541111
31fi7170_t:31517328
a1ije391_t:31533808
api_cot_off:31509852
g4a0e106:31510899
8hfba999:31537718
prpt_lrg:31513637
jbcp_cls_pctr_t:31531130
3f904173:31522231
cp_intellij_t_nes:31533504
gf14b233:31526830
hide-eh-duplicates:31543293
h561g132:31534507
replace-eh-with-ah:31544220
ihg5j128:31534457
f412h606:31543414
```

### Attachments