As long you're okay with sites that are just getting off the ground; the site I'm co-running; Shadows of Our Youth is available. Apologies for the rant! If you want, my PM's are open;
both links to the site and discord are in my signature too! In terms of some of your requirements:
slice of life ✓(ish) / modern setting ✓Our setting is our world, but in 2014 abilities and powers have always been a thing since before the dawn of the first epic tale of a character doing incredible feats. (Like Gilgamesh, or or beowulf, or any myth or legend back in the day.) It's just that for the longest it was all kept secret until a shadow war spilled out of of the shadows about ten years ago.
easy to digest, simple lore ✓Our lore is simple; secret war between two kinds of ability users happened, it became not a secret anymore, lasted for three years before it was stopped, as a means of making peace and trying to not have more wars break out schools for people with abilities were formed. It's been ten years since then. Everyone's pretty much used to powers and magic just being a thing in their everyday lives now. There's a few other things we've put in or left out with strings around to pull on but that's for you to decide whether or not you want your characters to dive down that rabbit hole in role play or not.
Supportive and understanding staff ✓ I'm dumb and I'm slow to catch on to things so bet your ass I'm gonna be patient and as helpful as possible.
Original setting ✓ I'm mean, we're as original as you can get considering we're the equivalent of an animanga super powered school RP? Granted we're not just the school, there's stuff outside of the school, towns/cities, forces at work around the school and around the world. Mercenary groups (wait whaaaat? Yup, find out in RP), we also love anime tropes at least I do and so do a few of the other admins so we have weird shit that'd you'd only see in an anime like a necromancer's skeleton construct having his own personality and doing things while dressed hella 70's disco esthetic,
WITH AN AFRO and we got a member spit balling how to make the ring yokai a ghost that haunts the school as a goth anime yandere girl. Yes, you read both of those correctly.
I think the only thing I would say isn't technically original, and is technically adapted from a fandom is our power system and
even then I had to spend so many days simplifying things and balancing it and just generally nixing all the complicated things about it and then make it work for the site. (Index/railgun/accelerator series btw, do not suggest. My god I had to take a full week to recover from that whole convoluted and complicated mess.)
Jcink ✓ We're Jcink, we like the features there, skins and stuff are better optimized, speaking of the skin is nice, was a purchased skin from Timeplapse over on tumblr. We liked the toggleable light/dark and we especially loved the fact that the skin was in fact mobile friendly.
Original characters ✓ Yup, that's really all we have. However I will say that if someone can actually manage to take a character from a random anime fandom and rebuild them to fit into our lore and setting well then; more power to them? As long as the face claim isn't already taken that is lol.
famlial, romance, long-drawn out story based plots ✓We got people who share those interests and are all;
About it.
Lax activity checks ✓We don't have those, pretty sure I and the other admins all stopped with that around in the early to mid 2010's.
friendly and open community ✓Yup, got that, we like to joke, we like to chat, we also like to pick on each other sometimes too but only playfully (If that's not something you're cool with just let the peeps know) We also don't judge people, not on their rp not on their gender identity, sexuality, nada. The only thing you might be playfully judged on is your taste in anime and food choices.
Big discords ✗Currently on our discord group we have -goes to count because he forgot- 12 people, of those 12 only like the most active chatters are myself, our main admin, and like three or four others but there's lulls in conversations where nothing is said and there's people that just pop in occasionally to say hi or hang out. Point I'm trying to make is we actually have the opposite of a bustling discord filled to the brim with so many people saying so much stuff you can't think because of all the pings.
stat based, stat focused roleplays. ✗The closest thing you get to that is our tier system for powers and our point system. Which is used to upgrade tiers, for right now, other things will be added. Promise. Even then the tiers are there to represent your character's skill / knowledge / experience with the powers they have at a glance than a hard fast; "hey this person is stronger than this person" type of thing.
unoptional/mandatory combat. ✗We don't force people into anything, including fights, I mean heck if you want no one is going to complain about you making a character who specifically
runs away from fights you won't be forced into anything on the boards unless you wanna be.
no panfandom. ✗Last one I was on in 2011 left a bad taste in my mouth and I've never been back to that style of site nor made one since. This isn't one of those.