Possible double refund situation with an airline

About a month ago, I bought a flight to Europe for late April via Air Italy. The total was about $1k.

On Thursday Feb 20, we noticed by reading the news (not from the airline) that the airline had issued a press release on Feb 11 that it was liquidating its assets and international flights would be cancelled well before the time of our flight. They recommended reaching out for refunds in the press release.

We try calling but they don’t pick up, so we leave an email requesting a refund. We try calling several times each day (to account for the timezones) and still never get through after 30 minutes of hold time, after which the call would automatically end.

By Sunday Feb 23, we still haven’t heard back from the airline so we follow an article that recommends disputing the charge with my credit card.

On Monday, we make a last ditch effort to contact the airline and finally someone picks up, informing us that they are working on the refund and it may take up to 14 days to make it to my card. Relieved to find out people still worked there and that the refund was in progress, I tried to contact my credit card to cancel the dispute, but found they were closed. I made plans to call them during business hours again. Before I could get in touch with my credit card, I found that my credit card had already credited me for the price of the tickets and had filed a claim against the company on my behalf.

I tried calling the airline tonight to request cancelling the refund, but after 30 minutes they didn’t pick up. I don’t want to end up with two refunds in my account. I suppose I have three options:

1. Call my credit card tomorrow to cancel the dispute. One potential risk is that the airline may have already cancelled my refund, or they may not have the funds to refund me, since they are in a bankrupt/liquidation state.
2. Continue trying to contact the airline to ask them to cancel the refund and instead settle things with my credit card company through that process.
3. Do nothing and assume it’s up to the airline to double check that no chargebacks or credit card disputes happen while they are in the process of refunding.

I am located in the US. Is there a proper response for a consumer in this scenario?