Modifier key to change the action of the side scroll wheel on Logitech MX Master 3 mouse

Keep on wishing.
Sorry to be the bearer of bad news, but the MXs are a nightmare because they hide the actual keycodes sent. I regret ever buying one. Standard 3rd party mouse control replacements, Steermouse, USB Overdrive etc cannot handle the extra scrollwheel or the gesture button. You can't even run Logitech's CP and one of the replacers, because they fight. You can run one of the replacers instead of the Logi, but you actually lose overall functionality.

You're stuck with whatever Logitech give you.

The mouse can be configured in great detail with the supplied Logi Options software. Your modifier key wish is called "Duolink" in the software. The modifier key is Fn in this case.

If desired, this can even be done individually for each application.

For example, I like it when the thumbwheel in the browser provides horizontal scrolling...

...and then switches through the tabs with the Modifier Key, e.g. when I hold Fn.

Have fun with your MX Master, I do not know any better mouse until now.