I'm also just realizing that inspection with dev tools is easier said than done. I just saw that you can at least find the tooltip text under "aria-label" on the element.
In example for a button with a tooltip "Search entities":
<ptcs-button class="ptcs-wrapper widget-content widget-ptcsbutton" tabindex="0" id="root_pagemashupcontainer-5_ptcsbutton-280" variant="primary" icon-placement="left" content-align="center" role="button" mode="icon" aria-disabled="false" aria-label="Search entities"></ptcs-button>
To style the tooltips you have a small section in the StyleTheme for it: Elements -> Information -> Tooltips.