FilePicker doesn't open at FullScreen

[Antreesy]

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Steps to reproduce

1. Open chat
2. Toggle FullScreen
3. Click on "Share from Nextcloud"
   

Expected behaviour

FilePicker should be visible

Actual behaviour

FilePicker is mounted by default at body, so same issue as with Viewer
We either can:

• set container with https://github.com/nextcloud-libraries/nextcloud-dialogs/blob/4ec4aa2f22e73e7e7a9a32e90af01cb55a7b0181/lib/filepicker-builder.ts#L134C1-L134C1
• migrate to using a component: https://github.com/nextcloud-libraries/nextcloud-dialogs/blob/main/lib/components/FilePicker/FilePicker.vue

⚠️ Haven't tested with stable27 yet