So according to the first three sources I find on the web, Jest appears to be the most used testing framework for React. Mocha could be interesting to look into also as it is quite popular too and I know that is used by Hardhat for example. So maybe it could be more suited for the blockchain aspect of it.
For now, as I don't know any of both and as we already have tests written with Jest I would suggest that we start by updating them and understand the possible limitations of the framework before digging into another one.
https://www.browserstack.com/guide/top-react-testing-libraries https://www.testquality.com/blog/tpost/tf857kfsl1-react-testing-best-frameworks-libraries https://fe-tool.com/react-testing-frameworks
So according to the first three sources I find on the web, Jest appears to be the most used testing framework for React. Mocha could be interesting to look into also as it is quite popular too and I know that is used by Hardhat for example. So maybe it could be more suited for the blockchain aspect of it.
For now, as I don't know any of both and as we already have tests written with Jest I would suggest that we start by updating them and understand the possible limitations of the framework before digging into another one.