CircuitBreakingException on my ES cluster

You have way too many shards.

Total shards: 1676 (90% indices are configured to have 5 shards per index. Largest shard is 814.6mb)

You should re-index every index that has 5 primary shards down to a single primary shard. That will make the cluster much more stable.
If you do that and the circuit-breaker issue persists, further possible causes can be explored, but the re-sharding needs to happen anyway.