How to draw on a PDF on Windows and save the changes?

I need to mark up a PDF with freehand notes, circles, arrows, and a few simple shapes without changing the original text. When I open the file in a browser on my Windows laptop, the pencil or drawing tool is not always easy to find, and I’m unsure whether the annotations will remain after I save and reopen the PDF.

Is there a free way to draw on a PDF on Windows with a mouse or stylus, adjust the pen color and thickness, erase unwanted marks, and save the annotations? Can this be done reliably in Microsoft Edge or Chrome, or would a dedicated desktop application be more suitable?

I’d be interested to know which approach works best for this kind of everyday markup.

Thanks in advance.