Update an existing host, add it as member of one more host group.
Visit audit and you will not find it's reflected. 

Confirmed using 7.0.7rc1.

Note - 6.0.37rc1 works correctly and does the audit!
So this looking as a regression.

There is a mystery case ZBXNEXT-6998, developed too long, opened before 7.0 has been released. I'm not sure it should be umbrella for this particular regression, so opening this as a separate issue.