No. Playnite's own requirements say Windows 10 or 11 and there is no Linux build. Lutris and Heroic do a similar job of gathering games from different stores into one library.
Playnite by Josef Nemec · Gaming · No way to run it
Playnite is a Windows program. The project states its requirements as Windows 10 or 11, and no Linux version
exists. It is built on Windows desktop technology with no Linux equivalent, so this is unlikely to change.
What Playnite actually does for you is worth separating from the app itself. It gathers games from Steam,
GOG, Epic, Xbox and others into one library with cover art, so you are not opening five launchers. Linux has
its own answers to that problem.
Lutris is the closest in spirit. It tracks games from several stores and from your own files, handles the
compatibility settings each one needs, and shows them in one grid. Heroic Games Launcher is narrower and
tidier, covering Epic, GOG and Amazon Prime Gaming. Steam itself can show games bought elsewhere in your
library, which is enough for a lot of people.
Your Playnite library is a list, not your games, so nothing is lost. Expect to rebuild the list once on the
new machine rather than importing it.
Free, and the nearest thing to Playnite. Collects games from several stores and from your own files into one library, and sets up what each one needs to run.
Your files: Cannot import a Playnite library file. You add your games again once.
Steam can add games you bought elsewhere to its own library, which is enough if you mainly wanted one place to press play.
This doesn't have to stop you
One stubborn program doesn't have to decide the whole question. You can keep Windows on the same PC and restart into it only when you need Playnite. Everything else you do can move.