If CCC is not working try booting into Safe Mode as you may have some third party software that is interfering with the process. It is best to run CCC with all other apps closed to minimize problems. There has to be a reason CCC is not working. An issue with third party software or a hardware issue are the most likely causes for CCC not to work. I've used CCC for 20 years with our organization's Macs and have never had a problem except when a Mac had a hardware issue. Unfortunately you haven't provided any specific details on the failure for anyone to assist with CCC.
You may want to create a bootable macOS external drive with a full installation of macOS. Boot from this drive so you can run CCC from it so you can clone the internal drive to another external drive. If this does not work, then you have an issue with your computer, external drive, or file system (assuming you are using CCC properly to make the bootable clone -- I assume you are if you used it in the past). The only change to a bootable clone with CCC is with Big Sur and Monterey where you need to erase the destination and right-clicking or Control-clicking on the destination within CCC and selecting "Legacy". I haven't used CCC v6+ yet, so maybe CCC now requires this for Mojave as well?
FYI, some things in a drive's health report may not show any "Warning" or "Failing" notices, but may still provide clues. SSDs usually require a manual inspection & interpretation of the health report.
Try running the Apple Diagnostics to look for other possible hardware issues.
Unetbootin is an app for creating a bootable USB stick from a specially created raw image file, like creating a bootable Clonezilla USB stick.
Rescuezilla and Clonezilla do have options for cloning drives bit by bit although they have severe limitations, but would be fine if cloning to an image file (to restore to the original source drive) or a destination drive of the exact same size as the source drive. You cannot use them to clone to a smaller destination drive. If you use them to clone to a larger drive, then the drive will have lots of wasted space. Sometimes it is possible to adjust the partitions to be able to access the empty space, but it is dangerous and does not always work especially with macOS since there are no apps/utilities to do this properly (even with Windows or Linux this can be tricky). Definitely more work & more technical to fix than getting CCC to work, unless you don't mind the wasted space. I've personally never cared for those tools for cloning as they just never met my needs for any situations I've had, although they do have some cases where I'm sure they are fine.
Only CCC and SuperDuper have the capability of cloning the same drive you are booted from (I've never had time to learn SuperDuper although I did try it once years ago -- much preferred the ease of use of CCC). Being able to clone the drive currently booted is actually very unusual since you usually want to clone a drive while booted from external media since the contents of the drive are continually changing if it is active.
If you want a macOS only option not involving third party software, then consider performing a clean install of macOS to the external drive, then migrate from a TM backup or migrate from your internal drive during the initial setup of the new OS.
