I'm not sure what's happening; I'll describe it the best I can. I have cCleaner 6.08.10255, Google Chrome 109.0.5414.120 and Microsoft Edge 109.0.1518.70 (Official build) (64-bit). I open my cCleaner, click the Analyze button, and it starts 'reading' (or 'searching' or whatever it does). It gets about halfway though my hard-drive, and seems to get 'caught on something' (I left it scanning for like a half-hour, but the scanning didn't advance past 46%).
I made some changes to the settings of my Edge (so I might 'reboot my computer' and see if that clears things up).
As you say you click the 'Analyze' button I'll assume you are using Custom Clean.
At the top of the results window it should tell you what it is looking at when it gest stuck.
It will be helpful if you can let us know what that is.
(Once you have it just close the stuck CCleaner using the 'X')
For example this is at 75% of the Analyze, and it's looking at the Firefox Site Preferences files:
If it was stuck there then you could simply untick 'Site Preferences' for Firefox so that CCleaner wouldn't try to clean them, but that wouldn't be fixing anything.
(Although you might want to do that anyway just to check that it's the only place that it's sticking at).
So if you can let us know where it's sticking we can then work out just why it's sticking there, and fix the issue.