You should document any verbal or phone conversations you had with the manager and the owner on the Airbnb messaging. "Just to reiterate our phone conversation yesterday, you told me...."
See how it goes as far as them actually giving you a partial refund.
If they aren't forthcoming with anything reasonable, then you can contact Airbnb- at the point you'll have written proof that you tried to work it out with the host first, which is the normal Airbnb protocol- a guest should always give the host an opportunity to deal effectively with an issue, and if the host won't, or can't, or their suggestion is unacceptable to you, then you talk to Airbnb. Or if you just don't want to put up with this any longer, ad would be okay with moving to another place, ask Airbnb to help you with that.
And even if the host comes up with something amenable to you, Airbnb should still be told about this- it's poor hosting on many levels.
It's hard to know what's going on as far as who has been responsible for this, the manager or the host. I suspect that the host is pretty hands-off, maybe just deals with the bookings and messaging with guests and leaves everything else in the hands of the manager. Who sounds pretty incompetent and may even have lied to the host about offering compensation to divert blame for managing things so poorly.
@Mohammed214