How to get Pages settings to function?

Then if they are on in the true sense of the word and not doing what you expect, then I would ensure that the spelling and grammar correction are not set to automatic, but rather to your specific language.

In Pages Edit menu > Spelling and Grammar > Show Spelling and Grammar panel, change the Automatic by Language to your specific language. In my case, that would be U.S. English. Selecting Grammar on this panel is optional.

And again, in that System Settings > Keyboard Edit… panel, Spelling should not be set to Automatic By Language either and should match what you have set in the preceding paragraph.

Yes, your description "checked off (on)" is uncommon and threw me. To me things are either off or on, but not in the parenthetical context that you provided.

Pages auto correction is not as advanced as Microsoft Word, or Grammarly's free Mac application that I use.

Pages is designed to take hints from the operating system too. Visit System Settings > Keyboard > Input Soures [ Edit… ] and switch off Correct spelling automatically, and Capitalize words automatically.

Visit Pages Settings > Auto-Correction and confirm that you have deselected Correct spelling automatically and Capitalize words automatically.

With a Pages document open, visit Edit menu > Spelling and Grammar and uncheck anything currently checked on that submenu.

These three paragraphs should resolve your Pages issues that you mentioned.

You are welcome.

The language settings automatic by language has been the default for years, most likely because someone in the product team thought that users would be writing multi-lingual documents.