Yes. Typora sells a Linux version alongside the Windows and Mac ones, as a Debian package or a plain binary, and your licence covers up to three devices.
Typora by Typora · Notes & PDFs · Has a Linux version
Typora's download page lists Linux builds for Intel and ARM machines, offered as a Debian package or a
direct download. There is also a community package on Flathub, though that one is not verified by Typora.
The licence is the thing to check rather than the software. Typora is paid, a one-off charge of about
fifteen US dollars, and a licence covers up to three devices. If Windows and Linux both count against that
allowance you may need to release the old machine from your account before activating the new one.
Your files are safe either way. Typora edits ordinary markdown files, which are plain text, so the documents
themselves open in anything. Copy the folder across and carry on. Custom themes live in a settings folder and
can be copied too.
The app behaves the same on both systems. What you type appears formatted as you go, with no split preview
pane, which is the whole reason people choose it.