Mikhail Ivanyushin recently published a script to enable in InDesign to deal with page breaks within tables as easily as what he likes to be able to do in MS Word. Mikhail’s demo video on Youtube shows in details its functionalities (no sound since the author comments are displayed in bubbles during the video), so does the pdf manual.
So DivideTableRow.jsx enables you to split a table row so that it begins at the bottom of a page and continues at the top of the next one [▶ 01:21]. Of course this process is reversible at will [▶ 01:40] and visually preserves the paragraph alignment parameters [▶ 01:47]. The script also enables to unmerge merged cells (again to allow page breaks) while preventing appearance of new unwanted horizontal borders between resulting cells [▶ 03:33]. Mikhail also studied the issue of table rows with alternating fill [▶ 07:01], whose logical pattern is broken when a table style is applied after a row was divided, so he added to his script a functionality to restore the logical color alternance by applying the same color to the divided row on both sides of the page break. The script works as well when a table is spread on several text frames/columns on the same page instead of several pages [▶ 07:50], and warns you in case of text overflow [▶ 08:09]. The script processes easily tables including header or footer [▶ 08:35]. The latest script update (04/26/2021) is about cases where some table rows are so high that they don’t fit in a single page [▶ 00:24]. See some users’ feedback.