I'm in social sciences and I've nearly always (bar two articles) published using empirical data so bear that in mind...
As a PhD student, I'd work on writing one paper at a time and focus on impact and contribution to the field. Remember quality over quantity - one four-star publication is much better than four one-star publications.
That's not to say you should only publish one paper during your PhD, you might have other ideas in mind. But write one at a time and concentrate on embedding and evidencing originality, significance and rigour - these are the criteria papers are judged on for REF.
Once you have submitted that first one, you could then start on the next one while you wait for an answer. But this, of course, needs to be balanced with writing your PhD as well.
I'm not too familiar with the thesis structure you're talking about of a building argument, no empirical data etc. But if you find that you have a lot to say but not enough for a full monograph, or you don't want to wait until after your PhD to get going on a monograph, then publishing companies do shorter book versions (25-50K words) which could work well. Here's Palgrave Pivot as an example: https://www.palgrave.com/gp/campaigns/palgrave-pivot
Most definitely think about publishing your MA dissertation. Data two years old isn't out of date at all as long as you're not talking about a rapidly changing field or population. I'm currently writing two papers - one based on data from 2020, one based on data from 2019. I would get in touch with your MA supervisor about it, but do some legwork before approaching them - scope out some potential journals and even potentially put a draft together in the right format (i.e. journal word length, standard sections etc.). Again, this needs to be balanced with writing up the PhD.
I would also talk to your PhD supervisor about your thoughts/plans for publications. S/he should be able to give you more specific advice.