You can do it all within PD but you have to be clear on what you're willing to sacrifice by changing to a vertical video. You can squeeze everything horizontally so it will all completely fill in the new frame, or you can shrink the clip so everything fits without distortion but you'll have large black bars at the top and bottom with no content. You can also crop the sides and use only one vertical section of your clip. here's what they each look like:
The first 2 options only require a single edit but each has visual drawbacks. Also, the second one would let you put text or other photos/videos above and below which might work for some projects.
The third is the best quality, but it will likely involve keyframes to keep the focus on the main object if there's any movement left or right as the video plays.
All of these choices are available in the PiP Designer, and for each one you'd drag one of the blue dots and drag it to resize the video as desired.
For #1, click and drag the blue dot in the center of the top or bottom frame until it reaches the edge of the visual frame and release it. This will stretch the vertical content which is the same as squeezing the horizontal.
For #2, click and drag one of the corner dots inward until the clip exactly fills the horiziontal visual frame.
For #3, click and drag one of the corners out and away until the clip fills the vertical visual frame. You may then need to slide the clip left or right to center the preferred section.