We have a 9 hosts (3 per pod) cluster with 1 pool in EC 5+3 (host domain failure),

That configuration is optimal for maximizing recovery times and write latency: since each EC set will span 8 hosts of 9, every time a host becames unavailable virtually all PGs will become degraded, and even with all host available any write will involve nearly all hosts. This kind of optimal configuration is popular with those who think that the original design assumption of Ceph of having many, many more hosts and OSDs than the replication factor or stripe width was wasteful and cowardly. :-)

I expected that shutting down 1 pod

Is there any particular reason why the failure domain is host but pods with 3 hosts get shut down?

wouldn't affect our pg but I just discovered that the EC pool is in min_size 6 while trying it. Is min_size 6 important in this case ?

Depends for what. But it is difficult to say without knowing the expected data and workload profiles. I might opine that in most cases it is as unimportant as having 'min_size=2' with 'size=3'. :-)

Could I safely lower it to 5

"Safely" and 'k=5' with 'min_size=5' is an interesting association :-).

or using another EC k+m would suit better?

Perhaps 'k=2,m=2' or for the very brave 'k=4,m=2'. But again it all depends on expected data and workload profiles.