swc-node | Faster ts-node without typecheck | Runtime Evironment library

1. How can we help SWC understand CSS (or mock CSS modules)? - SWC doesn't understand css natively, and neither did Babel. As you noted, when you were using Babel, the plugin styled-components took care of this. You'll need to do the same with SWC. I can't find an existing SWC plugin that does this, but you can roll your own. Obviously this is a pain, but such is the cost of using new tooling.
2. How can we help SWC understand absolute imports? - The .swrc options for baseUrl and paths should do what you want, but that, too, seems to have some issues.

You may have better luck creating issues directly in the @swc-node GitHub repo, but given the comments there it feels like you might be SOL for a while. Might be faster/easier to rewrite your tests using one of the libraries that Next supports out of the box.