I thought the ideal order was brush, floss, mouthwash.
There's not really a 'good' time to use mouthwash. Maybe an hour or more after a meal, if you're in a rush - but no sooner than that, as the tooth enamel will still be softened by the food.
So, mouthwash before toothpaste. Or do as I do, and use mouthwash intermittently when in the bathroom, to boost the time there is fresh fluoride inhibiting bacteria on my teeth and gums.
Most importantly, don't rinse after either - same idea.
What does an "oral microbiome" even mean? I understand what it means in the literal sense, but would a person's mouth be dysfunctional if it were hypothetically devoid of microbes? Is there an accepted healthy oral microbiome composition?