PbtA’s “core” isn’t its mechanics, but its principles (though some might disagree). Some of these core principles are:

• Play to Find Out: Don’t decide before hand what happens or do tons of prep.
• Fiction First: If a rule wouldn’t make sense in the fiction, ignore or bend the rule to fit the fiction.
• Have a Conversation: Talking to each other is a very important part of the game. Without it, you are basically just playing a boardgame, but with room for many misunderstandings.
• Fail Forward: Every roll should move the Story forward, leading to something interested. Never just outright fail.

===== Dungeon World =====

Dungeon World is a great game. Though it is a little of a mixed bag if people like it or not. I would say it has its flaws, but I would still enjoy playing it as is. Though, I do mostly play a hacked (house ruled) version of it.

The “trap” with Dungeon World though, is that people who are coming from DnD might fall back on old habits due to DW sharing genre and feel with DnD. And DW, or any PbtA, does not play well when people have that mentality.

These articles explain pretty well how DW is meant to flow. And that flow should be universal for any PbtA you try out (Glitter Hearts, BitD, MotW, etc.).

• Dungeon World Guide : Good guide to give an idea of how the game flows.
• 16 HP Dragon: Great example of how important the fiction is, and how "fiction before rules".

If you really want to break away from the DnD mentality, there is this neat article about creating the story as you play with the players (The Strandberg Recipe)

Basically the GM comes to the table with nothing more than an idea and some loaded questions. Three core questions should establish:

• An interesting location
• A looming danger
• A call to action

What the players answer becomes truths and the premise of the starting adventure.

===== Avatar Legends =====

Regrettable, as the rules are, I don’t have any advice. Normally a PbtA game uses the same rules/principles. It doesn’t have extra sub systems to keep track of. But Avatars combat does.

I have some ideas on how to house rule it to flow more naturally, but never gotten gone into putting it on paper. But I will say that if you have the interest and passion, I don't think the rules would be a hindrance.

===== Girl By Moonlight =====

I haven't looked at Girl By Moonlight that much, but it does look neat. But unfortunately, Blades in the Dark (BitD) and games based on it, have felt rather mechanically heavy for me. I must admit that I haven't tried one. Only read the books. So take my words on that part with a grain of salt.

But on paper when I compare BitD to other PbtA games, there are many more bits and pieces to keep track off. Almost like a mix of DND and PbtA.

===== Favorit System =====

I think Monster of the Week is a good representation of the principles of a PbtA. It is a action-horror game inspired by Buffy: the vampire slayer, x-files, M.I.B. And other similar series/movies. It has some very good sections describing how these games usually flow and how the GM and players are part of telling the story rather than the GM being the one doing all the work.

It being my favorit, might also be colored by the fact that during a very tough GM burnout on DnD, it helped me find the joy and passion for TTRPGs again.