I thought it was generally said that Google will favour 1 page per domain for a particular SERP, but I have seen examples where that is not the case (i.e. Same domain is ranking 2 different pages on the 1st page of the SERPs...) Are there any "tricks" to taking up 2 first page SERP positions, or am I mistaken that this doesn't always happen?

I’m struggling with a client website that's massively failing to rank. It was published in Nov/Dec last  year - not optimised or ranking for anything, it's about 20 pages. I came onboard recently, and 5-6 weeks ago we added new content, did the on-page and finally changed from the non-www to the www version in htaccess and WP settings (while setting www as preferred in Search Console). We then did a press release and since then, have acquired about 4 partial match contextual links on good websites (before this, it had virtually none, save for social profiles etc.) I should note that just before we added the (about 50%) new content and optimised, my developer accidentally published the dev site of the old version of the site and it got indexed. He immediately added it correctly to robots.txt, and I assumed it would therefore drop out of the index fairly quickly and we need not be concerned. Now it's about 6 weeks later, and we’re still not ranking anywhere for our chosen keywords. The keywords are around “egg freezing,” so only moderate competition. We’re not even ranking for our brand name, which is 4 words long and pretty unique. We were ranking in the top 30 for this until yesterday, but it was the press release page on the old (non-www) URL! I was convinced we must have a duplicate content issue after realising the dev site was still indexed, so last week, we went into Search Console to remove all of the dev URLs manually from the index. The next day, they were all removed, and we suddenly began ranking (~83) for “freezing your eggs,” one of our keywords! This seemed unlikely to be a coincidence, but once again, the positive sign was dampened by the fact it was non-www page that was ranking, which made me wonder why the non-www pages were still even indexed. When I do site:oursite.com, for example, both non-www and www URLs are still showing up…. Can someone with more experience than me tell me whether I need to give up on this site, or what I could do to find out if I do? I feel like I may be wasting the client’s money here by building links to a site that could be under a very weird penalty 😕