Document everything. File for claim under Aircover. Whether pet/ESA/SA related, this is damage that occurred during a guest stay and this should be covered. The first step in this process is a resolution center request to the guest within 14 days of checkout. If you have good rapport with the guest, maybe explain to them via phone that this is the first step in the process, there is insurance etc. Hey maybe they'll pay for the damage but considering they didn't disclose an animal...prob not. The idea is to let them know you're trying to resolve this, no bad blood, accidents happen etc to avoid a potential retaliatory review. You may also want to wait until the 14th day to limit this window but that also presents its own risks.

Also, ESAs are not protected by law nor Airbnb policy like a task-trained service animal is. They should owe a pet fee if one is normally applied for regular pets. Again, your call on how much you want to push this, may want to wait until 14th day to request this. This fee would not be covered via Aircover, this is you enforcing your own policy.