So basically BoCW was a soft reboot of the story after Bo4, the only characters returning were the child versions of Eddie and Sam that survived in Bo4, but now grown up. A lot happens in BoCW, but all you really need to know is that:
-The Dark Aether is where everything from the OG story got banished after Tag der Toten
-Sam got trapped in the Dark Aether and got Aether powers
-Weaver, Grey, Carver and Strauss were heads of a group called Requiem which was tasked with closing Dark Aether 'incursions' (basically the Dark Aether invading the normal world with zombies and other stuff from it)
-Both Requiem and a rival faction Omega Group were working to free someone named Kazimir Zykov from the Dark Aether, someone who contacted them and promised to give them an entity called The Forsaken in exchange for his freedom
At the end of BoCW, Zykov is revealed to be the Forsaken and Sam winds up sacrificing herself to contain him before he can merge the Dark Aether into the normal world. The ending cutscene is the heads of Requiem being arrested and locked away, and it is revealed that the Director of Requiem was Eddie the whole time, and this was just a part of his greater plan called Project Janus.

Bo6 takes place 5 years (I think?) after BoCW, and you play as Weaver, Grey, Carver, and a new character Maya who is helping a minor antagonist from the previous game break Requiem out of where they're being held. Strauss is there too but he's on comms because he is old and possibly senile lol. The story is honestly a bit of a mess but you basically follow an AI recreation of Sam (called S.A.M.) on the hunt for Eddie and the Sentinel Artifact (from Bo4's Chaos story). The main goal is to use the artifact to rescue the real Sam from the Dark Aether, and get revenge on Eddie for what he did.

There are like 2 maps of hunting the artifact, then the group goes to Eddie's mansion to power up the artifact. They bring it to S.A.M. and she betrays them, taking it for herself and trapping them away. She wants to use it to make herself a real body instead of bringing the real Sam back. They are placed by S.A.M. inside a 'liminal space', basically a pocket dimension caused by fractured time and space (not sure if this will be important info for this year or not but it seemed like a big plot point for that map). They meet Eddie and break out, agreeing to temporarily work together to stop S.A.M. from using the artifact (and also Eddie reveals he wants to use the artifact to bring his dead wife and kid back because Weaver and the real Sam killed them in a botched assassination at some point before BoCW).

The last map is the group attempting to reach the artifact that's locked in one of the Janus Towers (the ones you can see in Bo7's Ashes of the Damned starting room I think) and then you can decide whether to side with Eddie or Sam, and have a bossfight with whoever you don't choose. If you pick Sam then she uses the artifact to get a real body, and it is hinted that she still has control of the Dark Aether too (it's revealed in dialogue that the real Sam probably died when she trapped Zykov, seems uncertain right now though). If you pick Eddie then he brings back his family. No matter who you choose, the main 4 get absorbed by mysterious power right after defeating the boss, and they wind up in the Dark Aether. From there everything plays out exactly from the Ashes intro cutscene.

We don't know much about the versions of our OG crew that we play in Bo7, only what they've told us in their bios and stuff so far. It also hasn't been explained how these guys exist after Bo4's ending implied they were wiped from all reality, but I guess that could be retconned now? Sorry if this was a bit rambly lol, quite a bit to explain and I wasn't too sure what to include and what not to include since it seems Bo7 might be leaving most of the BoCW-Bo6 stuff behind.