I suspect there is logging of graphical command operations.
Where are those command logging files for Linux Mint and CentOS?
Thanks.

Smarta-alec'y answer:More correct answer:There is history of commands within your terminal. Graphical commands? You mean mouse clicks and screen actions? None natively in any Linux OS, nor (to be fair) Windows. I was aware of a screen spy utility, but it was an add-on that people could put on a screen to monitor/catch/spy/etc probably not technically legal and so forth.

Brute force would be to run your system, mouse around a lot and check files, as well as hidden files and verify that things aren't growing. You're internet cache file will grow, but you can look at that.

Your question is open ended, doesn't really explain your thinking, perhaps you can share why you feel this and what the impetus is for your question. I mean, if you're all paranoid, then I recommend you become very well versed in Linux, enough so that you can make this determination yourself. I won't tell you that it's impossible, I've already cited that persons could install software (previously known for Windows) which can do that, I've seen software which can take screenshots every so many seconds, therefore whatever content someone is viewing, it is all saved, provided it's showing at the time of the screenshot. That typically would be used for spying, likely on spouses or kids, "for the greater good" as the perpetrator would always tell you. I.e. not morally good. Only you can determine if this situation potentially matches your own.

If instead you're just asking because of a technical thing, like you need to record and replay a sequence, I'd say again, "not natively", and also add that if you're trying to automate something, there are likely better ways to do it.

Being able to see the command issued after graphically setting or interaction can enhance command line learning significantly.

If the gui app issues a command, it has to go through Bash. and Bash interprets and then sends relevant command to kernel. So somewhere this command may be logged (or should be logged?) globally.

No it won't go through the shell. The UI is running a program and uses the library calls available to it. For an example, you use mv to rename a file, correct? Please take a look at the C program manual page for the rename() function, which is a library command used from within a program to accomplish the same action, thus without the use of the shell ever.

rename(3)

But these operations has to go through the kernel somewhere inside those C function calls if it involves the filesystem or some kernel level operations.

But it won't go through BASH per your assertion. Note that you can find the C code for the rename() library function and determine what that does. And you can also find the C code for the mv command and determine what that does. Likely they do very similar stuff, but no guarantees. This is just one example, there are others. And remember that there are usually more than one way to skin the cat, hence a UI program uses library functions more than uses any BASH commands, especially since using a BASH command would require a fork() to accomplish it and would be very inefficient versus just using a library command. I do not believe this is either uniform, or as simple as you're trying to hope it can be so that you can put in a single hook to be able to conclude everything from a single source.

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you can check the kernel calls using strace

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