Learn Russian: Третий указ готов, пускай они прочитают текст. - The third decree is ready; let them read the text.

In this context, there is no difference in meaning. Both are particles used to mean let or have someone do something. Пускай is simply a more conversational or colloquial version of пусть. You can use either one to form this third-person command.

Why is прочитают in the future tense if the English translation is let them read?

In Russian, third-person commands about completing a specific action are formed using пусть or пускай plus the perfective future tense. Because reading the text is a one-time, completed result they want to achieve, we use the perfective verb прочитают (they will read). The particle пускай turns this future-tense verb into a command.

Why does this sentence use готов instead of готовый?

Готов is the short form of the adjective готовый (ready). In Russian, short-form adjectives are used when the adjective acts as the main state of the sentence (the predicate), like is ready here. Short forms are especially common when describing temporary states.

What case is текст in here, and why didn't its ending change?

Текст is in the accusative case because it is the direct object of the verb прочитают (they will read the text). However, because it is a masculine inanimate noun, its accusative form looks exactly the same as its nominative dictionary form.