Use Frames and link them, or, if your texts are short, use tables.
In the OO extensions repository there are some templates for various scripts - play, film etc.
See
https://templates.openoffice.org/en/search?query=script&sort_by=created&sort_order=ASC for a selection. One of these might suit you "out of the box".
It is often best to use Tables; limit your tables each to one page if possible. Tables have the advantage that the texts, shown in separate columns, are easily aligned. Usually in any form of scripting the texts are short.
Apache OpenOffice 4.1.7 on Xubuntu 18.04.3 (mostly 64 bit version) and very infrequently on Win2K/XP