To narrow this down, could you please confirm whether you have any additional Logitech software installed, such as Logitech Options or SetPoint, alongside Logi Options+? Also, does the setting revert immediately when you change it through Windows Settings, or only after restarting when Logi Options+ is running? These details will help determine whether the problem is caused by conflicting software or Windows failing to retain the preference.
As an additional troubleshooting step, I suggest temporarily preventing Logitech's software from loading at startup. Press Ctrl + Shift + Esc, open Task Manager > Startup, locate Logi Options+ and any other Logitech configuration utilities, and select Disable. Then restart Windows, open Settings > Devices > Mouse, and change Select your primary button to Right without opening Logitech's software. Restart once more and check whether the setting remains saved. If it does, this would suggest that a Logitech background process or configuration is overriding the Windows setting. If it still reverts, Microsoft's recommended next step is a clean boot to identify possible third-party software conflicts.
https://support.microsoft.com/windows/experience/startup-boot/how-to-perform-a-clean-boot-in-windows.
Please let me know the results of the startup test to determine the next step without repeating the procedures you've already tried.