How does zombie spawning/mutation strength actually work in Civilization VI?

As mentioned in the earlier answer, some of this is actually answered in the in-game Civilopedia:

It's Melee Strength increases with each Zombie that has been eliminated globally. If a zombie destroys another unit, a new Zombie unit spawns in that tile the next turn.

And this is confirmed in the online Civilization Wiki

So Mutation Strength goes up by 1 every single time a Zombie unit dies, and a Zombie will spawn next turn any time a Zombie kills a unit.

Going and carefully re-watching the February 2021 Game Update Developer Livestream has answered the rest of my questions here.

In the Livestream the Devs explained a number of other ways zombies spawn:

• Every Barbarian Camp initially spawns "2 or 3" Zombies in addition to it's usual Barbarian units.
• Any time a unit dies (to anything, not just Zombies), there is a chance a Zombie will spawn in that tile later. The Devs say there is a "5 turn and 50 turn" chance, but that for destroyed Zombies "the length of time is even longer".
• When a Zombie attacks a City Centre tile there is a "low chance" that the City population will go down by 1 and an extra Zombie will spawn in an adjacent tile.
• Finally, they explained that killing a unit with a Zombie unit that is under your control (from any source) will spawn another Zombie unit that is not under your control.

So I must have been misattributing the Zombies that spawned when my Zombies killed other units (like the waves of attacking Zombies they killed on Defence) as unexplained extra Zombies because they spawned after the Barbarian turn alongside all the other hostile zombies spawning. It also seems that the "friendly zombies create more unfriendly zombies" thing is not a bug, but is actually the intended behaviour.

No wonder my first Zombie Defence game quickly degenerated into a hopeless World of The Dead situation...