Thanks again for bringing this up and opening this, I think you should be able to put interactive elements into titleText and have them work as expected. It looks like the Toggletip contents never shows because focus is immediately being moved to the Dropdown for some reason.

Hi, just happened to encounter this same bug still in v1.75.0

I believe the cause of the bug is because the Dropdown component is utilizing the html element <label> tag to wrap the titleText property. https://developer.mozilla.org/en-US/docs/Web/HTML/Element/label from the documentation:

When a user clicks or touches/taps a label, the browser passes the focus to its associated input (the resulting event is also raised for the input). That increased hit area for focusing the input provides an advantage to anyone trying to activate it — including those using a touch-screen device.

This is most likely why, the focus initially is on the Tooltip, but it is quickly overlapped by the label's property of shifting that focus over to the input.

Those lines are here: 613-617

        {titleText && (
          <label className={titleClasses} {...getLabelProps()}>
            {titleText}
          </label>
        )}

Whereas other components like the TextInput re-use the Text component for their labelText.

const label = labelText ? (
    <Text as="label" htmlFor={id} className={labelClasses}>
      {labelText}
    </Text>
  ) : null;

Not sure if there is any difference in these properties or why they are labeled differently, both properties have the same description: Provide the text that will be read by a screen reader when visiting this control

Edit:
Just noticed the Text component has as='label', I can see the input being highlighted first, then the focus shifts to the toggletip