I’m not sure how broad this category is - look what happened with roguelikes - but it does bleed over into RPGs and, when RTS was a thing, there were a fair few Real Time Tactics games knocking about, with little to no resource or base management. I have particularly fond memories for the original Ground Control, for example. In my personal experience though, the real-time games lean less upon the individual and impactful decisions that Into the Breach is almost entirely focused on, and they do tend to play up the management layer instead. Less life-or-death decision making, more looking for efficiencies that pay off in the longer term.
It’s hard to say what really got me on board with the genre - I’ve dabbled in a lot when I was younger, from the old x-com games, Chaos Gate, a fair few RTT and the real time stealth/puzzle focus of commandos - but I think Strategy RPGs were the gateway, Final Fantasy Tactics being the first one I played. And every so often, you would be at just the right level and squad setup, and the game would go just badly enough, that it would feel like a very roguelike, and for a few turns it would be a life-or-death struggle where every action counted - and that’s what I find the best feature of this as-yet-unnamed genre. I’ve no idea how Into the Breach would be to a complete newcomer, but it trades heavily on that exact situation.
As to ironman, I can’t say what anyone else should do. I find it a combination of a long, bad book with a great ending, and a nutritious yet horrible vegetable. If there’s a big time investment required, unless I’m playing as a kind of social thing and talking about it with other people, the prospect of everything going pear shaped over the course of a few bad missions and killing a run is too offputting. However great the individual moments of my campaign, I’m unlikely to go back.