Can we still set a "highlighting mode" in Preview on the Mac (for PDF documents)?

I remember in the past, we can double click the "highlighting icon" and make it a highlighting mode, so whatever we select in the PDF document, it'd be highlighted permanently. Select something again, and it is again highlighted permanently. (highlighted as if it is marked by a highlighter).

But now in Mojave, it doesn't seem to have this mode? We have to select something and move the mouse to click that highlighting icon, and select some text, and move the mouse to click that highlighting icon again?

This behaviour still works for me in Mojave: Preview's Toolbar has a highlight icon. When active (the lighter colour seen in the image below), then you can highlight text in the way you describe.

The behaviour you're seeing may be what happens when the highlight icon is not active (the same shade as the other icons).