Creating disk image: Operation failed

I solved this problem by manually adding "Disk Utility" to the list of applications that have Full Disk Access.

Open Settings>Privacy & Security>Full Disk Access

Click on the ➕ icon at the bottom of the list to add an application to the list.

Navigate in the dialog box to /System/Applications/Utilities/Disk Utility.app

It will ask if you want to close and reopen Disk Utility. Approve and you should be good to go. (Assuming that you had the same problem as I did.

Where is the destination image located? You cannot put the resulting .dmg file onto the same drive you are trying to image. Make sure to select the internal boot drive or another external volume for the destination of the resulting .dmg file.

Disk Utility is not very good about making images of physical devices or volumes. Sometimes it can be done with smaller volumes, but I usually avoid Disk Utility as it doesn't work very well. I'm not certain if it can make an image of an exFAT volume as I have never tried it. I recently tried to make an image of a very small bootable volume for a utility I use, but that failed (at least when using Ventura).

There are some third party apps available which may be able to do this for you. I know Carbon Copy Cloner and SuperDuper are two options. I know a co-worker likes to use another small app for creating images of larger folders like the home user folder....I think it is DropDMG, but I'm not certain. macOS/Disk Utility can mount all resulting images created by these apps.

If you are familiar with the command line, then it is possible to make a raw image file as well, but the third party apps are probably the better & easier option for most people.

I haven't used Clonezilla recently and even years ago I only tried it once or twice, but it was not a good option form my need to clone at the time (usually needed to move to a smaller drive). I don't recall exactly how Clonezilla works anymore, but I believe it did perform a bit for bit clone as one of the options. Any option I have for a similar clone involves using command line utilities which can be riskier since it is so easy to select the wrong destination or make a mistake. macOS includes a native command line utility which can be leveraged to do this as long as the source drive does not have a hardware failure (I think it utilizes the same method Clonezilla uses, but without a GUI interface). I actually use a Linux system or boot drive to perform my bit for bit clones since it includes a command line utility which is able to deal with the errors of a failing drive unlike most other options. I'm not familiar with any paid apps which may perform a similar function especially on macOS since the macOS "cloning" apps work at a file level and not at a lower block/bit level (there may be paid Windows apps though which will perform a block level or bit level clone...I've never looked since the open source utilities have been great for me to do this).

Keep in mind doing a bit for bit clone requires the same or larger size drive as the destination.

Personally I like to send the raw data to a raw image file which I use as a backup of the original drive. Then I will either make another copy of the image file and work from the copied image file, or I will send the data from the image file to yet another drive (same or larger size than the original). This allows me to quickly start over if I make a mistake trying to fix the file system or if something goes wrong. Part of whether I go this extra bit is if a hardware failure is involved or the recovery involves taking risks. Not all repair/recovery tools work well from a mounted image though.

All of the apps work on a file level by copying files.

If you want a block level or bit for bit copy in order to perform data recovery, then the only tools I'm familiar with are command line based utilities. Command line utilities are risky to use if you are not familiar with the command line since you could mix up the source & destinations by overwriting something important.

It really helps to know all the details of what you are trying to accomplish here.

Not sure if it will make any difference, but there are several options you can choose when creating a disk image read only, compressed, read/write, etc. Which one(s) have you tried?

All of the options I mentioned will put the image into either a .dmg file or a .sparsebundle file both of which are native Apple archives which macOS can open without any third party apps.