Wow this was a mess. Needs PowerShell/PowerShellEditorServices#2130, and I'm a little worried about breaking changes but supplying "current" to processId is special-cased to still work (well, throw an appropriate warning), since the launch configuration types only generate warnings.

Ok so we removed the notion of IDs (which are integers) being strings because that broke serialization with recent updates. But on inspection we realized the whole point was to be able to say "current" and have the attach configuration attach to the currently running Extension Terminal. Except that this was an unsupported, half-baked scenario (sure, it attached, but it couldn't actually be debugged properly). So now that throws warnings in both the client and server. The defaults for processId and runspaceId where changed to null (again, now they're just integers) which means to query for them. The supplied but half-baked configuration was removed.

Fixes #4843

LGTM

Still happening to me in a code --profile-temp with the extension installed from vsix. I checked the source zip and the JS looks to match the PR

  async pickPSHostProcess() {
    await this.getLanguageClient();
    const items = [];
    const response = await this.languageClient?.sendRequest(GetPSHostProcessesRequestType, {});
    for (const process3 of response ?? []) {
      let windowTitle = "";
      if (process3.mainWindowTitle) {
        windowTitle = `, ${process3.mainWindowTitle}`;
      }
      items.push({
        label: process3.processName,
        description: `PID: ${process3.processId.toString()}${windowTitle}`,
        processId: process3.processId
      });
    }

Let me try it in extension debug

From Code Review

Now also resolves the root of #4699.