Under the current applicable cancellation policy you were not entitled to a refund, because an inability to travel because of Covid related travel restrictions isn't an 'extenuating circumstance'.
It's clear that regardless of the prospect of a refund, you were not able to travel and therefore the host's offer to refund you is not what induced you to change your travel plans.
What has happened is that you incurred a loss, the host initially offered to absorb the loss on your behalf but then changed their mind. The question is, 'why'?
This type of behaviour by a host is extremely unusual, so I'm wondering if perhaps you said something that might have made the host change their mind.
Is it possible that after the host kindly offered to refund their share of the accommodation fee you berated the host for the loss of the Airbnb service fee, or perhaps you simply didn't thank them for their kind offer? This happens, more often than I care to remember. There have been several occasions when I've taken the hit for the guest only to regret it because of their subsequent behaviour. If I could have taken the money back or stopped the transaction I would have. Have you been 'that guest'?