There are no calls to curl_global_init() and curl_global_cleanup() in Zabbix code. It's probably worth adding a few. Quoting libcurl documentation (bold is mine):

If you did not already call curl_global_init(), curl_easy_init() does it automatically. This may be lethal in multi-threaded cases, since curl_global_init() is not thread-safe, and it may result in resource problems because there is no corresponding cleanup.

You are strongly advised to not allow this automatic behaviour, by calling curl_global_init() yourself properly.