SUMMARY
When opening a new PDF that okular never seen before (so no file specific settings), the view mode always has "Continuous" disabled despite the setting "Open in continuous mode by default" being set.

So on every new PDF I open with Okular, I need to enable the Continuous mode manually.

STEPS TO REPRODUCE
1. Open Okular and enable setting "Open in continuous mode by default" in menu "Settings -> Configure Okular"
2. Open a new PDF that Okular has never seen before. The PDF is a normal single column PDF.
3. Check "Continous" mode: in the toolbar, click on "View mode", "Continuous" should be checked but is not.
4. Scroll pages, when switching pages it jump to the next page, meaning "Continuous" mode is effectively disabled.

OBSERVED RESULT

3. Check "Continous" mode: in the toolbar, click on "View mode", "Continuous" should be checked but is not.
4. Scroll pages, when switching pages it jump to the next page, meaning "Continuous" mode is effectively disabled.

EXPECTED RESULT

Openning a new PDF should set "Continuous" mode by default if  "Open in continuous mode by default" is set.

SOFTWARE/OS VERSIONS
Operating System: Debian GNU/Linux 12
KDE Plasma Version: 6.3.2
KDE Frameworks Version: 6.11.0
Qt Version: 6.8.2
Kernel Version: 6.12.17-amd64 (64-bit)
Graphics Platform: X11
Processors: 4 × Intel® Core™ i5-3230M CPU @ 2.60GHz
Memory: 7.6 Gio of RAM
Graphics Processor: Intel® HD Graphics 4000


ADDITIONAL INFORMATION

I've checked the source code, and I suspect the commit "036b037d8ceb521213293ea6765c62037b0616e1" Support pdf Default Page Layout.
Related bug: https://bugs.kde.org/show_bug.cgi?id=188239