@Katelyn68
I’m sorry to hear the incident happened.
Obviously, the guest is being difficult to you. Enforce to you for a full refund or else to leave a negative reviews in your listing.
You are doing well and right with your efforts to offer a dinner to the guest.
Short power outage and power off for 8 hours was definitely not under your control. It is not necessarily for a full refund.
You can try to communicate with the guest with the maximum of one night refund or the dinner offer thought to the “ Airbnb Resolution Center” by sending the payment.
Meanwhile, doesn’t matter the guest agree or refuse your suggestion.
Please do acknowledge to the Airbnb Support Help Center immediately, “ live Chat” with the Airbnb Ambassador ( not an Airbnb bot )
Usually, you will have an answer from them within minutes.
Do report to the case manager for the incident happened and request them to save the file to protect your right or to avoid future complaint from the guest and resolve the problem immediately.
In addition, contact Airbnb via social media Twitter, Facebook for attention with fast respond.
You can find more detail to contact via Airbnb by following the below link :
https://community.withairbnb.com/t5/Help/Contact-Airbnb-A-Community-Help-Guide-UPDATED/m-p/413245
Hope you can resolve with your guest soon