[JetBrains] Make backend-plugin compatible with 2025.2

[mustard-mh]

Description

Related Issue(s)

Fixes CLC-1407

How to test

• Build success
• Integration tests pass - tests are using stable version of IDEs because code changes affect stable plugin as well, and they are the ones that matters https://github.com/gitpod-io/gitpod/actions/runs/15434746261/job/43438832233?pr=20871

Test manually

• Start workspace with stable IDEA and WebStorm
• It should work and tasks terminals are working well

Documentation

Preview status

Gitpod was successfully deployed to your preview environment.

• 🏷️ Name - hw-jb-eap
• 🔗 URL - hw-jb-eap.preview.gitpod-dev.com/workspaces.
• 📚 Documentation - See our internal documentation for information on how to interact with your preview environment.
• 📦 Version - hw-jb-eap-gha.32968
• 🗒️ Logs - GCP Logs Explorer

Build Options

Build

• /werft with-werft
  Run the build with werft instead of GHA
• leeway-no-cache
• /werft no-test
  Run Leeway with --dont-test

Publish

• /werft publish-to-npm
• /werft publish-to-jb-marketplace

Installer

• analytics=segment
• with-dedicated-emulation
• workspace-feature-flags
  Add desired feature flags to the end of the line above, space separated

Preview Environment / Integration Tests

• /werft with-local-preview
  If enabled this will build install/preview
• /werft with-preview
• /werft with-large-vm
• /werft with-gce-vm
  If enabled this will create the environment on GCE infra
• /werft preemptible
  Saves cost. Untick this only if you're really sure you need a non-preemtible machine.
• with-integration-tests=jetbrains
  Valid options are all, workspace, webapp, ide, jetbrains, vscode, ssh. If enabled, with-preview and with-large-vm will be enabled.
• with-monitoring

/hold

[iQQBot]

Tested both IDEA and Webstorm