Does anyone have experience regarding importing theatrical text scripts (with correct formatting) into Dorico, so that one has the theatrical text directly together with the songs in a Dorico file?
Which screenwriting software (Final Draft, DramaQueen…) would be recommended?
Do I have to insert the final theatrical text page by page as an image (.jpg) in Dorico or are there better possibilities (i.e. Text directly editable in Dorico)?
You are definitely going to want to do up your music and then insert it into the text file in another program (acrobat, preview, etc.). It will be very frustrating and slow to try and insert a lot of text pages into your score directly in dorico.
Although Dorico is adding a certain amount of text formatting to its text block, it is (IMO) definitely not the way to present a script with music. @Romanos is correct that another sort of program (whether something like InDesign or a simpler PDF program) is the way to go.
I would say the same thing were you to be working in Finale, and I imagine the same would be true for Sibelius.