I was able to reproduce the issue on Firefox 112.0a1 (2023-02-16) on Ubuntu 22.04 Wayland where multiple prompts were shown initially. The issue is fixed on Firefox 111.0b6 and Firefox 112.0a1 (2022-02-26) and only one prompt is shown from Firefox then the xdg one and the screenshare starts. Tests were performed on the same Ubuntu 22.04 Wayland system.
Bug 1817263 Comment 15 Edit History
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I was able to reproduce the issue on Firefox 112.0a1 (2023-02-16) on Ubuntu 22.04 Wayland where multiple prompts were shown initially. The issue is fixed on Firefox 111.0b6 and Firefox 112.0a1 (2023-02-26) and only one prompt is shown from Firefox then the xdg one and the screenshare starts. Tests were performed on the same Ubuntu 22.04 Wayland system.