How do I pass text containing utf-8 new line characters as a value to a parameter for a REST request

you can use the percent-encoded value for a new line, it's %0D%0A although %0A(ASCII 10 - line feed) or %0D (ASCII 13 - carriage return) should work alone.

https://stackoverflow.com/questions/10601672/posting-url-with-string-parameter-that-contains-line-breaks-using-java

Also disable URL encoding of the parameter value for the REST resource/method when using custom encoding in this case.

For custom encoding handling when setting a parameter value (the “Disable Encoding” setting)

https://www.soapui.org/rest-testing/rest-resources-and-methods.html