There are thousands of worldwide 'arrangements', 'protocols' and 'reciprocal agreements', these aren't trade deals. The EU and the UK didn't say 'Oo look we've just signed 10 trade deals with Japan, both countries announced 1 trade deal.
OK, you and you're assistant are keen on pointing out that Australia doesn't have a trade deal with the EU, and this is true, but amongst those 759 agreements that the EU have signed worldwide, dozens of those are with Australia.
So by your logic. the EU has multiple trade deals with australia.