Pages and Numbers won't open to chosen template or to template chooser.

My Pages v14.4 on an M4 Mac Mini Pro or my 2020 Core i7 iMac, both running macOS Sequoia v15.4, opens to a Template Chooser. My operating system and Pages are installed on the startup drive. My Pages templates are also stored in the Pages container area. I have not assigned my Desktop and Documents folder to storage on iCloud.

Your quick fix is to select Pages File menu > New and that should open a Template Chooser.

Since you had already performed what I suggested to the iCloud Settings panel, and what is usually the cure for the File .vs. Template Chooser issue, I don't have any other recommendation for a fix other than the following in order:

• Shutdown
• Reboot into Safe Boot mode (See Apple Silicon steps)
  • Press and hold the shift key while launching Pages
    • That suppresses it from loading its last saved execution state
  • File to Template Chooser presented?
• Reboot normally
• Test if Pages now opens to a Template Chooser

Visit System Settings > iCloud > [ See All ] and deselect Pages and Numbers there. That will restore the initial Template Chooser when launching these applications. It also hides the Pages and Numbers folders that these applications create on iCloud Drive with these iCloud settings enabled.

The Pages Settings > General should remain as Show Template Chooser.

Tested: Pages v14.4, Sequoia v15.4.