Hi Yu,
I could not find any direct way to increase the width of "TabGroup" in the App Designer.
However, I found that there is a toolbox in MATLAB File Exchange that supports changing the tab width and has some more customisations:
You can download the GUI Layout Toolbox and install it into MATLAB to use. You can create a "TabPanel" using "uix.TabPanel" and then change its "TabWidth" property.
Another workaround is to create button group and overlay it over the tabs as described in this answer.
Hope it helps.