On the evening of Saturday 21 April, I will need to take a taxi out of the Serra de Estrela to the train station in Mangualde (in order to catch the Sud Express to France). I'm not sure where I will take it from. From Seia, Gouveia, or Covilhã, I'm quite confident I'll be able to find a taxi. But I might end my hike in Manteigas, which is much smaller and located in the middle of the park. Should I expect to be able to find a taxi in Manteigas on a Saturday evening?
You will most probably get a taxi easily; while Manteigas is small, it has a good road accessibility for getting out of Serra da Estrela.
However, please note that Manteigas is on the opposite side of the Serra from Mangualde. It would be more sensible, nearer and cheaper being in Seia or Gouveia, if you could change your plans.
Taxis also work pretty much any time of the week or day (or night). The location is however small, and you might have to call them by phone. On the other hand, being the location small, you might also be able to walk to the "Praça de taxis", where usually 3 to 5 taxis are waiting for customers.
It might be wise booking a time and place to be picked up for improving your chances of getting on time.
Searching in the Internet, this seems to be the number of a local taxi service: +351 275 982 868 - Táxi de Silva Carvalho & Monte
If hosted in a local accommodation, ask them to call/book the taxi for you, they will be more than happy to help you.