dbcc failing with Cannot continue the execution because... alwayson having a change of state event for each db
I have experienced this behavior before, where the AGs "blip:"


from PRIMARY to RESOLVING and back to PRIMARY
from SECONDARY to SECONDARY


It's my understanding that, on a system with a small number of logical processors (1-4), and with multiple AGs (or AGs with many databases), some of these "blips" are unavoidable.  Especially if the server is a VM with even slightly noisy neighbors.

Availability Groups use a lot of worker threads baseline.  You can read about the thread requirements for AGs in detail here: Thread Usage by Availability Groups

I'd suggest that you avoid having other CPU-heavy scheduled tasks run at the same time, in order to reduce the risk of these events occurring.  In this case, it looks like index maintenance was running at the same time as CHECKDB.  If you have a big enough window, try to spread these out so they don't overlap.