No, an externality is an impact you create that isn't a part of your business model. It can be positive or negative. Most of the time people talk about negative externalities these days, especially with airlines, they're talking about profiting from climate change. (Although I don't know that Ryanair is worse than anyone else.)

So if we priced airlines in regards to all of their externalities, they would have to pay for climate change but would get a portion of the all revenue derived by business trips (ie. the time saved traveling by air compared to other modes of transport and what the employees traveling would have been able to produce during that time). I wonder if they would end up better off under that system.

They’re already capturing those benefits - they are among the reasons customers buy tickets and thus contribute to the price.

I’m sure positive externalities are a thing, but direct benefits to one party in a transaction aren’t externalities.

In the same sense the climate change effects are also priced in as most people in the west use air travel or add enough carbon via other means to have to be personally responsible for any ill effects.

In the OPs example, hiring low wage labor, is in fact reflected in the price.