Can I transfer a video project (PC 1) that has been processed with Nero 2019 to another PC (PC 2) and continue editing with Nero 2021?

Yes, you can copy project and source file from PC1 to PC2.

If project was created by lower Nero version, it can open in higher Nero version; If the project was created by higher Nero version, it can not be open in lower Nero Version.

So you can open project in Nero 2021 and edit, if the project was saved by Nero 2021, it can not be open in Nero 2019.