How can I set font size relative to button size in Custom Button Card?

I have a dashboard using Custom Button Card, designed for use on an Android phone. When the phone font size is increased for readability, the text in the dashboard buttons increases in size, but the buttons remain the same. This causes the text to outgrow the buttons.

I’ve tried setting the font sizes in the dashboard in units of em, px and %. None of these seem to make any difference to the behaviour on the phone. I also tried vw %, but that apparently doesn’t work at all.

Is there a way to set the font size to stay in proportion to the displayed size of the dashboard buttons?