Frankly, this is probably not worth the time and trouble that it will take to set it up.
Time Machine backs up your entire Mac by default.
Time Machine Preferences / Options gives you the ability to Exclude items from backup, so to do what you want, you basically will have to Exclude everything else on the Mac from being backed up. That is going to be quite a task depending on where your Client Files folder resides and you have your Finder files set up.
It will not be that difficult to Exclude major folders..... things like Applicatons, Pictures, Music, Documents, etc.....but to get to the point where you want may not be that easy.
Take a look at things by opening Time Machine Preferences, then click on Options
Since you will be adding items to be Excluded, you would need to click the + button at the bottom of the window and then navigate to find the general folder that you want to Exclude.
Unfortunately, you cannot simply tell Time Machine to only back up the items that you want.....you have to tell Time Machine what NOT to back up.....which is going to be most of your Mac.
And.....whatever you set up in Time Machine /Options to be Excluded will apply to all backups to all Time Capsules. You cannot specify what is Excluded on one Time Capsule and not another. It's all or nothing. Not what you want to do, I am sure.
Good luck 😉
