Firstly, since this is a temporary situation just download Visual Studio 2019 Community and use it. It is free and you can add the SSIS extension to it. You don't need a formal license. To download it you'll need to go here. Once the SSIS extension is updated then you can remove Community.
AFAIK you cannot use a newer VS product key on an older version. If you have a VS Subscription then you'll use your subscription instead of a key and you then have access to the older versions as well. But if you just have a VS 2022 product key then you must use VS 2022.
Again though, SSIS extension is going to be updated and, while there isn't a release date yet, it will probably be coming sooner rather than later. There is no real benefit in getting a VS 2019 product key (or downgrading your existing key). If for some reason you don't want to use Community edition then you can install VS 2019 Pro as a trial. You can extend it up to 90 days so surely by then the SSDT team will have updated their extension as everyone is waiting for it. Here's a link to information on trial versions of VS. But Community is free...