[BUG] @typo3/backend/tree/page-tree-element does not work in BE-Modules

[dkd-kaehm]

BE-Modules produce the BE-Links with strange id parameter, which leads to exceptions.
typo3/module/searchbackend/index-administration?id=0_1_500_501

How to reproduce:

1. Chose some EXT:solr BE-module
2. chose some page in tree
3. switch to another EXT:solr BE-modules, or other page in tree and again to EXT:solr BE-modules
4. See the error in Browser-dev-tools->Console

   Uncaught (in promise) SyntaxError: identifier must be of type string 
   at ModuleStateStorage.update @_assets/081fa96a07de1dccb64a8a83e1567439/JavaScript/storage/module-state-storage.js?bust=1727170979:13:128 (real file: typo3/cms-backend/Resources/PublicJavaScript/storage/module-state-storage.js)
   at ImmediateActionElement.connectedCallback @_assets/081fa96a07de1dccb64a8a83e1567439/JavaScript/element/immediate-action-element.js?bust=1727170979:13:1624 (real file: typo3/cms-backend/Resources/PublicJavaScript/element/immediate-action-element.js) 
   

5. Switch to some Core Module with page-tree, the PID is not chosen as well.
   Chosing other page in tree solves the issue.

Source of trouble:

EXT:solr module do not provide module infos(identifier) in response, so the processing in

https://github.com/TYPO3/typo3/blob/0d6b6e7f9cf70058a6b8a8f7f2c903f69618f30e/Build/Sources/TypeScript/backend/storage/module-state-storage.ts#L43

  public static update(module: string, identifier: string|number, selected: boolean, mount?: string|number)
  {
    if (typeof identifier === 'number') {
      identifier = identifier.toString(10);
    } else if (typeof identifier !== 'string') {
      throw new SyntaxError('identifier must be of type string'); // <- Here stops the processing
    }
    if (typeof mount === 'number') {
      mount = mount.toString(10);
    } else if (typeof mount !== 'string' && typeof mount !== 'undefined' && mount !== null) {
      throw new SyntaxError('mount must be of type string');
    }
    const state = ModuleStateStorage.assignProperties(
      { mount, identifier, selected } as StateChange,
      ModuleStateStorage.fetch(module)
    );
    ModuleStateStorage.commit(module, state);
  }

Current workaround: Chose desired page in tree again to get int UID again in address-bar

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TYPO3 Core issues:

• https://forge.typo3.org/issues/103784
• https://forge.typo3.org/issues/104457