I think this is a little more nuanced than just say no.
ite not a breach as you know what it’s for and are giving permission by giving it.
it’s clear she wants it in case they have staffing issues to be able to call people on to cover.
so what is your issue, is it you don’t want people to have your number or you don’t want to cover anyone, even if you could.
id personally not just say no. But I’d explain the issue clearly ie if it’s just the number say no I don’t want it shared but you can have it if you need cover. You call me.
of it it’s you don’t want to provide emergency cover just say I am not providing the number as I am not willing to provide cover. In many workplaces this is problematic and can be seen as lack of team player, working to rule etc.
if it is really the latter and you pretend it’s the former you run the risk of saying ok I will keep it and I will contact you.and then you need to explain you’re not available
the other thing is, if it’s not an issue for it to be shared you can just not answer the call if it came through,