How to save a "List" column for later use?

Perhaps what you're looking for is to save the full response from the API as a binary, save it to the lakehouse as a binary and then consume the binaries through a different dataflow.
If this is in line with your expectation, I'd suggest raising a new idea using the link below:

 https://aka.ms/FabricIdeas

You could also post an idea for the lakehouse team to increase the maximum string size. As mentioned before, this is not a limitation of the Dataflow engine, but rather a limitation of the destination which cannot handle more than X number of characters for a string and how many characters your string has.

All of the previously shared solutions are the ways that you can handle things in Dataflows Gen2 today:

• Expand the complex values as those data types are not supported in the destination that you're mentioning
• Transform the complex values to a text string and save it as a string.
  • Furthermore, you could encode the string so it shortens things and save it that way. It could also make the number of character expand tremendously, so it might not be a one-size-fits-all solution

So this a limitation on the Lakehouse/Warehouse end.

I've opened an idea so they increase the Text field size.

https://ideas.fabric.microsoft.com/ideas/idea/?ideaid=fd452033-4bb2-ee11-92bd-000d3a0d7518

Please vote