Here’s the important bit about Charging and being engaged:
Here’s what Unstoppable does:
Here’s the part from Unit Charges that you reference:
Note that both Unstoppable and the Unit Charge section directly reference Disengaging. The quoted Unit Charges section above tells us – to summarize – that models in the unit who were engage prior to being placed Disengage as part of being placed during a Unit Charge.
And, as you can see, this language was essentially copy/pasted straight from Disengaging:
So, putting it all together:
If one model in the unit is not engaged, that model can be chosen to charge. (Source: Unit Charges.)
If the unit does not have Unstoppable, any models that Disengage must forfeit their Combat Actions. If the unit has Unstoppable, models can Disengage without forfeiting their Combat Actions.
The only special interaction with Charges is the opening quote showing that engaged models cannot charge. Otherwise, charging is treated identically to non-charging from this perspective.
(And, to make it clear: charging – the movement bit – is distinct from “making a charge attack”, as per this thread:
Immortals with ExtollerAdvocate charging Polarity Field model)