Do astronauts really have to pay for pillows and blankets as shown in Ad Astra?

I think you've entirely missed the point of the scene. It's trying to convey that in near future, space travel has become monetized; that, like most things on Earth, the interests of megacompanies are now dictating the rules of space travel, as opposed to the more selfless goal of prioneering science and technology. Note that it was meant to be a "commercial" flight to the moon, implying that perhaps private firms now fly rich people to space, with zero interest in scientific advancement and merely monetary benefit.

Broadly speaking, as commentary on the consumerist culture, sci-fi stories commonly tell of scientific achievements we dream about resulting in Mega-Corps finding extra means of controlling people and gaining power and money. In this example, we often dream of colonizing the moon or advancing so far in technology as to make space travel affordable to more people than just governments and Musk.

One possible outcome, if we were to achieve cheap space travel, is an advert-overloaded future (warning: TVTropes link) where private firms have made travelling to the moon only slightly less comfortable than travelling by plane. One possible source of revenue for such companies would be extra premium items the passengers can purchase. Soft pillows are not necessary for space travel — chairs can be redesigned if there are significant effects on the astronauts' performance — and they might be one such item.