Unable to restart IDE Frontend after Plugin Update

**Summary:** IDE Frontend restart (e.g., after Plugin Updates) is not successful. The IDE process is running, but the Frontend has never been restored.

**Steps:**

1. Open spring-petclinic project in Coder plugin in Gateway. IDE is IntelliJ IDEA 2025.3.
2. Update or install any plugin that requires an IDE restart (e.g., Spring or Docker).
3. From the Plugin screen, click on the `Restart the IDE` button and then on `Restart IDE Frontend`.

**Result:** Frontend never restarted. The process changed PID, which is expected, but the Frontend never opens again. Most likely, the new **join link** is not handled properly by the plugin.

Checked on Gateway 2025.3, but the issue can be reproduced in 2025.2 as well.

To collect the logs, I killed the process and reopened the IDE. Therefore, a valid Client folder to check the logs is:
`RemoteDev-logs-20251212-105853/anastasiya.stachnik/ThinClient/actual/2025-12-12_at_10-52-50
`
[RemoteDev-logs-20251212-105853.zip](https://github.com/user-attachments/files/24124744/RemoteDev-logs-20251212-105853.zip)

**Environment:**

JetBrains Gateway 2025.3
Build #GW-253.28294.342, built on December 8, 2025
Source revision: d3d8f1cb6210a
Runtime version: 21.0.8+9-b1163.69 aarch64
VM: OpenJDK 64-Bit Server VM by JetBrains s.r.o.
Toolkit: sun.lwawt.macosx.LWCToolkit
macOS 15.7.2
This IDE is managed by JetBrains via JetBrains IDE Services.
JetBrains IDE Services version: 2025.6.0.5328-ij253, https://tbe.labs.jb.gg
GC: G1 Young Generation, G1 Concurrent GC, G1 Old Generation
Memory: 2048M
Cores: 16
Metal Rendering is ON
Non-Bundled Plugins:
com.coder.gateway (2.23.0)
org.jetbrains.junie (253.549.30)
org.jetbrains.toolbox-enterprise-client (2025.6.0.5328-ij253)

まず、Coder plugin で「Restart the IDE」および「Restart IDE Frontend」までの Plugin 画面のフローを再現し、その後 ThinClient/actual/2025-12-12_at_10-52-50 にある添付ログを調査します。プロセスが PID を変更した後に、新しい join リンクがどのように処理されるかを追跡します。プラグインによって再起動がトリガーされた後に IDE Frontend が正常に開けば完了です。

索引モデルが issue の本文から書いたものです。