Hi @Sasho Zahariev ,
The feature to get alerted when there is an update on status page is currently not supported. I see this related feature request already raised in Uservoice or feedback forum. So I would recommend you to upvote it and other features that are of interest. In general, Azure product feature team would check feasibility of a feature request, prioritize against existing feature backlog, add in roadmap as appropriate and would announce and/or update the related Azure document once a feature request is addressed.
If interested, as a workaround you may try implementing something like this.