No. EaseUS Todo Backup is Windows software and EaseUS lists only Windows versions on its product page. There is no Linux build, but Linux comes with backup tools of its own.
EaseUS Todo Backup by EaseUS · Cloud storage & backup · No way to run it
The EaseUS Todo Backup Free page lists Windows 11, 10, 8 and 7 as the supported systems. Linux is not
mentioned and there is nothing to install.
The important thing here is your existing backups. EaseUS saves them in its own .pbd image file, and no Linux
program opens that. If those images hold the only copy of anything, restore the files you care about onto an
external drive while Windows still works, and check they open. A backup you have never tested is not really a
backup.
On Linux the same job is done by apps that come with the system or sit in the app store. Déjà Dup on Ubuntu
and Pika Backup on Fedora both copy your documents and photos to an external drive on a schedule and keep
older versions, which covers what most people used EaseUS for.
Whole disk images are the other half of what EaseUS did, and Rescuezilla handles that. It makes a copy of an
entire drive that can be written back if the disk dies, and it looks like an ordinary program rather than the
older tools it is built on.
The closest to the disk cloning side of EaseUS. Copies a whole drive so you can put it back after a failure.
Your files: Cannot read EaseUS images. Makes its own drive images.
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 EaseUS Todo Backup. Everything else you do can move.