I'm currently a player in something somewhat similar: a Salt Marches ("Marshes"? I've only heard it; anyway...) campaign on a dedicated Discord server. Characters live in D&D Beyond (one of the GMs splurged on "all the books", which was quite nice), but could live just as easily in Roll20; they could also live in a Google Doc or even as posts in the Discord server.

We have about a dozen players, some of whom have two characters. Each player is a member of a faction and has some reason to have come to "hubtown" (a lightly plot-armored village that acts as the hub of the campaign).

Each real-world week represents two in-game weeks. During an in-game week, a character can perform one downtime activity and/or go on an adventure (some adventures require downtime, some don't).

Downtime activities include:

• currying or spending non-faction favors (characters have a limit on these; they're less formalized than faction favors, and are generally intended to be used fairly quickly)
• gaining or spending faction favors
• gaining a proficiency
• making money
• buying/selling magic items
• doing explicitly plot-relevant things that don't fall into the above categories; eg.: we currently have a salvaged airship that we're repairing

Most of the downtime activities are in Xanathar's Guide to Everything; most that aren't are reskins of "make money", where the thing you're trying to do has a GP cost (eg.: repairing the airship requires 1,000 gp; I can either spend a week making bricks to earn 20gp then donate that to the ship - paying NPCs to do it - or I can spend a week working on the ship and earn 20gp towards its completion).

Adventures can provide gold, magic items, and faction favors with the various factions (and are the fastest way to gain any of the above, by far). Acquiring (not holding, but acquiring) sufficient faction favors increases your rank with that faction (it's theoretically possible to be a member of multiple factions, provided they're not opposed to each other). With higher rank, you gain faction benefits (eg.: my fighter has a ring that gives him a couple of cantrips and a bonus on checks using the Athletics proficiency that scales with his faction tier) and can turn in favors (and, potentially, gp/downtime) to gain more potent benefits (specific magic items, a feat, information, etc.).

In-character activities are encouraged between adventures. The GMs (there are 2) kick off some activities ("a mysterious stranger enters hubtown"), but players are encouraged to start their own, too.

Adventures use the full 5e combat system (non-adventure stuff theoretically does, too, but combat in town is frowned upon). They're run whenever a GM and 4-6 players (1 character per player, even for those with two) can agree on a time (generally, GMs propose 1-3 times and players vote). Adventures run over Discord voice chat and Roll20 for tactical stuff, dice rolls, etc..

Adventures are run "con-style": no cliff-hangers, with a fixed end time (though a sequel is plausible). The GM may elide an encounter entirely or abstract it by simply charging a few HP and maybe a spell slot or similar to get to the boss with enough time to run that encounter before the end time.

Everything that happens in a real-world week happens "during the two in-game weeks". Any character who wants to be involved in an IC RP event can be there even if their downtime activity would have them out of town for the whole real-world week. Downtime activities are locked in at the end of the real-world week, giving players a chance to respond to the results of an adventure or IC RP event.

XP progression is modified from 5e's standard. Gaining a level requires 100 XP, regardless of level. Every real-world week, a character can gain up to 30 XP: 10 for engaging in at least one IC RP event, 10 for performing a downtime activity, and 20 for joining an adventure. Characters who are below the average campaign level gain a 50% bonus (which can put them above 30/week) to help catch up.

I've been a member of the campaign for about 3 months. It's worked quite well during that time (with the occasional lull in activity, especially with Thanksgiving weekend here in the States). A lot of the people involved did something similar that ran successfully for at least a couple of years. So, a system like this can work well in the long-term.

Using fuzzy time per real-world week helps everyone stay involved at all times. Even if one character's downtime activity for a real-world month would have them out of hubtown, it's assumed that they were back for a visit whenever an IC RP event happened that they wanted their character to be involved in (even if travel time would be prohibitive, though the immersion-breaking aspect there is limited by putting most "out of hubtown" downtime activities in a larger city that's just a day or so away). In principle, a character could be gone for longer, but that's been handwaved thus far.

Simplifying XP lets those whose schedules don't lend themselves well to joining adventures still stay mostly caught-up with the rest of the group, which it sounds like would be especially important for the in-person sessions.

With Discord, you could have private channels for any relevant set of players, so their characters can plot without other players simply reading the chat (whether you'd want to isn't entirely clear from the question, but I got the impression that you might). And, of course, you can have an "other" channel or two, for chatting that isn't directly about the campaign. IME, having an "other" channel is critical to keeping the players engaged: if they can come and chat about whatever, they're coming back to that server and will see the channels that have new in-character stuff waiting for them; they'll also be reminded that they care about the story (hopefully).

There's no particular reason that an adventure couldn't be run for fewer than 4 players (or even for a single player) (or that such an adventure would have to go to Roll20 and use the full "minis on a map" tactical detail that that provides). The campaign that I'm in hasn't had any 1-on-1 adventures that I'm aware of, but there's talk of it in the campaign rules docs.

There's also no hard rule that says that the characters need to live in hubtown (though it's probably a good idea). They should have a reliable means of communication, but homebrewing a magic item that facilitates that would be pretty simple (from Star Trek style comm-badges to magic email/Discord). Letting the characters keep in reliable contact and have reasons to engage in in-character chat will (IME) strengthen their players' attachment to the characters and the campaign; it also helps with trickling out the plot. So: I'd recommend that they live in hubtown and make excursions further afield, but it's not a hard requirement (that said: could the characters' locales be regions within a city rather than far-flung cities?).