Taking Stephan's comment from Gerrit https://gerrit.libreoffice.org/c/core/+/98226: <https://curl.haxx.se/libcurl/c/curl_easy_init.html> explains that calling curl_easy_init (as is called from SearchAndParseThread::execute via curlGet) is delicate in a multi-threaded process: It calls curl_global_init if necessary, and that is not thread-safe, and may call non-thread-safe code in underlying libraries---and my assumption is that it calls non-thread-safe code in nss that then somehow caused the above use-after-poison. I suggest to make it experimental and suspend the unit test for now.
Guess this can be solved with https://gerrit.libreoffice.org/c/core/+/105169