Desktop Chrome test note: the embedded player stayed blank grey on my setup, so I didn't reach level 1. I couldn't see a start button or an error message. I saw the v13 update says it starts inside level 1—could you confirm which build should currently load in the itch embed? I haven't tried the downloadable ZIPs, so this is only a report of what I saw in the browser, not feedback on the gameplay yet.
Thank you, this report was really useful. The grey screen came from a third-party script loading in the page head: when your browser or network blocked it, the whole page never rendered, so there was no button and no error. I've just uploaded a fixed build that loads it in the background and starts the game anyway. A refresh should take you straight into level 1. If it's still grey, please let me know your browser and any extensions and I'll keep digging.