Correction. You used Design Science's MathType for years with Pages '09 and Pages v5 thru __ until Wirus acquired MathType and dropped further Pages support. It is still not available for Pages, as Wiris only provides it as a downloadable plug-in for Word on macOS. The full MathType beast from Wiris is now an annual subscription.
Apple has not kept its Pages documentation current, as it still suggests that one can use MathType 6.7d or later with Pages. That version of MathType is quite old, and may not be compatible with later releases of macOS, or Apple Silicon. Pages v11.2 on an M1 Pro running Monterey 12.0.1 still has that Preferences setting to alternatively use that old version of MathType. Good luck with that…
The LaTeX support in Pages is provided by a compiled converter (blahtex) application that translates some LaTeX commands to MathML which is what is embedded in the Pages equations using the default equation editor. One can even input direct MathML and it will also work. I have the full MacTeX distribution installed and it is not referenced by Pages at all due to this converter application. See Apple's Add mathematical equations to your document in Pages, Numbers, and Keynote.
If you still have the MathType 6.7d or later, try and use it. I doubt that Wirus is providing it as a free download any longer. Without it, equations will be entered into Pages using blahtex's restrictive support, or via MathML syntax. Or, if you can find an online Math editor that is easy to use, you may be able to download the result as PDF and drop that into Pages.