While it shouldn't include prestige classes that add +1 to existing spellcasting class, there are some prestige classes (i.e. assassin, sublime chord, suel arcanamach, etc.) that actually learn to casts spells and other prestige classes are used to progress their spellcasting. Here's a link to the Sublime Chord. Hence why the feat Obtain Familiar works for them.
https://dndtools.net/classes/sublime-chord/
EDIT: The script isn't adding any of the other arcane classes to the companion's level still. Went and started testing by adding Bard, Spellthief, and Warmage, but level didn't improve while Shadowcaster was at 5th level, so couldn't meet the prerequisite for any familiar at 7th level.