how to assign property value (of a response) to a variable, and re-use it in a new request?

Looks this is related to this other thread of yours. Have you tried with script provided there?

You haven't mentioned where you need to use the extracted value, by the way?
https://community.smartbear.com/t5/SoapUI-Open-Source/How-to-assert-on-value-in-a-Json-response/m-p/139172#U139172
It is even not sure what happened to other question as it is still open while many relevant answers were provided. If you found helpful answer or solved altogether please convey that. No response to the solutions provided to your earlier questions.

Regarding this question: you need to add another statement to script provided in the above thread.

context.testCase.setPropertyValue('TOKEN', parsedJson.accessToken.toString())

In order to access the TOKEN in other request steps, use property expansion ie., ${#TestCase#TOKEN}