Please Help, Modifier Keys Question

I bought a mouse with MANY buttons, it’s the Solakakka E9 Pro.

Its buttons are recognized as keyboard keys instead of mouse keys, they come with onboard memory to customize the buttons to the user’s preferences.

I’d like each mouse button to be recognized as a "F1, F2, F3,etc” key. And have BTT shortcuts for the “F keys” that LISTEN to the currently pressed MODIFIER KEY combinations.

So far, I couldn’t get it to work myself, BTT just receives the naked "F1, F2, F3” keys without the currently pressed modifiers keyboard keys. Even if I have the “use higher level key modifier recognition” feature ON. And the “use high-level mouse event recognition” ON as well.

This is the product’s website: https://www.kickstarter.com/projects/818470634/solakaka-e9-pro-your-best-grip-for-work-and-victory/comments
This is the product’s web application: 鼠标设置工具

I beliebe that this would be a common issue for every user that has a mouse with onboard memory profiles. I for the life of me can’t get it to work and would love to. Any help or advice is fully appreciated here. Below is a screenshot of the mouse’s button configuration: