I havent used soapui and jira with zephyr before, but ive used jira with zephyr (about 3 years ago) and ive looked at integrating soapui and testrail (which is another test management tool) so i can give you some general comments, but thats it.....the testrail/soapui integration might work the same as zephyr(jira)/soapui integration.
So..zephyr is a plugin and a standalone apparently that adds test management capabilities to jira. Essentially when i was using the jira plugin, it added some additional fields on an jira object page (which allowed you to link to test cases which could be created in jira....allowing us to link reqs to tests and audit the execution status of a test.)
Soapui with testrail works by testrail exposing a post rest api on the testrail application server. The way it appeared to work was that you create placeholder test cases within testrail that correspond to your test cases in soapui. Within soapui, within each test case you add in a rest post request that uses the testrail api and updates the corresponding test case in testrail with the pass/fail test case results. I suspect the soapui/zephyr(jira) approach will work the same as this or at least a similar manner.
UPDATE: as i said earlier in post, its been 3 years since i looked at zephyr and that was the free plugin for jira. The standalone works like a true testmanagement tool so you dont need jira for this option.
I hope this has helped, although i suspect it hasnt,
Theres probably more info on there about soapui if you look around
But in the end, isnt what you need to do constrained by what software is agreed to be used at your site? What i mean is, if no one is willing to pay the money for the standalone app, then all you can use is the free jira plugin anyway.
Am i missing something essential here?
What is currently being used? Or have you been told "we will be using zephyr, so readup"? Cheers