Using a program like Tabletop Simulator or one of the alternatives.
I'm thinking 40k because the 10th edition is right around the corner and I'm interested in using that as a jumping on point, but I'm open to playing anything - Age of Sigmar, Battletech, Warmachine/Hordes all come to mind as alternatives, but I haven't been active in the hobby for a long time so I'm sure there are hundreds of newer games out there that are great too.
My big thing is I really want to play a narrative campaign of something, not just match up with randoms to play one-off battles where we barely talk. All of the games I mentioned have rules for that, with stuff like your units becoming veterans over time and your characters being consistent.
Since it's online there would be no expectations of buying anything (or participating in the irl hobby at all) to participate. We could coordinate over Discord and do things like have multiple games going at once, change games in between campaigns, spectate battles and chat, etc.
The way I see it, campaigns would have a pretty forgiving schedule like "one turn per week", and the scheduling would be game to game since you and whoever you're playing against would have to arrange a time. That should keep things pretty flexible since not everyone has to be available at the same time.
It's more probably the mental load of figuring out a new system and maintaining a lance or an army. But flexible scheduling should still be helpful.