How to stop table from splitting across pages between rows (leaving gaps) in Pages

"…this is what worked for me: when you select your table and select Format pane > Arrange > toggle between "Stay on Page" and "Move in Text" and voilà it's fixed."

The significant part is not that you've 'flipped the switch,' but which state you left the switch in.

The image in your post shows the selected object set to "Move with text" and to be placed "inline with the text." With those settings, a table in Pages on my Mac moves downward on the page as text is added above it, and when the text above fills the available space, the table is pushed, a row at a time, onto the next page below. If there are header rows on the table, a copy of these is shown above the rows now on the second page.

If the Arrange panel is left in the state shown below, "Stay on Page", with text wrap "Above and Below,"

my table stays where it is placed on the page, and, and, if more text is added above the table, that text, or the text between it and the table flows past the table to the space below, and if necessary, to the next page.

Regards,

Barry