Yes. Blackmagic Design makes DaVinci Resolve for Mac, Windows and Linux, and your project files open on either system. The free version on Linux is fussier about some video formats.
DaVinci Resolve by Blackmagic Design · Video · Has a Linux version
Resolve is one of the few big creative programs with a proper Linux version from its own maker. Blackmagic lists
Mac, Windows and Linux on the product page, and the paid Studio version is available on all three as well.
Your work moves with you. Resolve project files and project libraries are the same on Linux as on Windows, so a
project made on the Windows machine opens on the Linux one. Your Studio licence key works on Linux too.
The honest catch is formats. The free version of Resolve on Linux does not handle some common camera and phone
formats, particularly H.264 and H.265 recordings, as smoothly as it does on Windows. For a lot of home users that
is the whole problem, because that is exactly what phones record. Buying Resolve Studio removes the limitation, and
converting footage first is the alternative.
Installation is also less automatic than most Linux software. Resolve comes from Blackmagic's own download page
rather than the app store, which means signing up and unpacking an installer yourself.