This is almost certainly a blocked print head. You can use the nozzle cleaning as much as you want but if the printer was left for any amount of time without being used the ink will have dried to a hard substance in the head unit. Epson use a none water based ink formula so soaking in water wont help either.
Best bet would be a replacement head unit but they look pricey. Here is the Google search, listing the show Shop items;
https://www.google.com/search?q=epson+xp-960+print+head&rlz=1C1CHBF_en-GBAU992AU992&sxsrf=APq-WBumc6KmgqrvG1_ecy8YNlmzdHBa9Q:1649078172938&source=lnms&tbm=shop&sa=X&ved=2ahUKEwj_q9H1vvr2AhVbSmwGHUNdCc4Q_AUoAXoECAEQAw&biw=1366&bih=625&dpr=1