Calling 3 a soulslike is kinda stretching it, I think. I would say rather that 3 does exploration and upgrades similarly to 1 but has combat that’s more similar to 2. I do think they’re definitely worth getting though.
2&3 are both “here’s what the others were doing while War was chained up for a hundred years”. Their stories are set in motion because of the premature apocalypse, and will probably have implications for humanity further in the future, but there’s no impact on War directly, aside from 3 implying
spoilerhow Strife lost his guns for you to get them in the first two games
, and I don’t expect any plot points from 2&3 to come back up during 4.
As for Genesis, the main thing you should keep in mind is that it isn’t a mainline game. It’s more an isometric twin stick shooter/hack’n’slash, and the gameplay isn’t as deep as with the main games. But it’s got co-op, if you have someone to play with, and it does provide some characterization for Strife as well as showing an example of the sorts of missions the Horsemen took for the Charred Council.
I actually played this long before I ever played actual Ninja Gaiden. At the time, I was just a wee laddie, and I remember enjoying it back then, but I’ve never had the courage to go back and replay it to see if it actually holds up.
Back in Control, all the stoplight did was teleport you back to the entrance if you moved on red. That’s way too easy for co-op though, so I’m sure Remedy changed it.