Hi ReuelAbi,
Thank you for reaching Microsoft Community.
I understand that you need to use the Tab key on the Mouse and Keyboard Center to set the Three Finger Click on the Arc mouse do Task View action. However, this is a limitation on the app itself. You may submit feedback on this to Microsoft to improve and add this function to the app through our Feedback Hub. See: Send feedback to Microsoft with the Feedback Hub app - Microsoft Support.
However, I found some old post where the workaround is to create a Macro for this. Try checking this old post I found from Social Technet forums which has a similar concern for the Tab key: Assiging ALT+TAB to a mouse button with the Microsoft Mouse & Keyboard Center? For more details and assistance regarding creating Macros, it would be best to post this concern on the Microsoft Q&A forums. There we have some skilled and knowledgeable users on this concern that can share their inputs and ideas on this. See: All Questions - Microsoft Q&A.
Kind regards,
Marrion