This was Andersen's age 33 season. He will want to get a long-term deal to serve as his last big deal before retirement.
Carolina will have a bunch of cap room next year. In addition to Andersen, they lose J. Staal, Fast, Stastny, Gostisbehere, Pacioretty, Gardiner, Raanta, and Kase, all to the tune of over $20 million. Puljujarvi is really the only RFA of note. Necas and Jarvis will need new contracts before the end of next year, so Carolina won't blow all 20 million this year. Amazingly, Svechnikov, Kotkaniemi, Slavin, Burns, and Kochetkov are the only Hurricanes under contract for 2024-2025. A lot of people will need raises or be sent away in the next couple years.
The answer to your question will probably be borne out by how free agency goes. If someone is willing to give Andersen 3 or 4 years at a salary comparable to his current $4.5 million, he takes that. But if the goalie market stagnates for Andersen, then he's probably looking at a one year deal with Carolina unless Carolina signs someone else first to pair with Kochetkov. He'll get the Klingberg treatment, which is worse for goalies. I don't see him resigning with Carolina unless the price point is low or the term is 1, or at most, two years.
Of note is that this year, each of Kochetkov, Andersen, and Raanta played around the same number of games and Andersen generated the worst GAA and SV% of the trio. Not by much, but that data point shows that Carolina doesn't exactly suffer if Andersen leaves.