If you are a freelancer then your contract should allow you to do work for others. In which case, your response to this client has to be "Sorry, but my business laptop potentially has data from other clients on it. I can't let you install this monitoring agent without violating my contractual confidentially agreement with those other clients. I always maintain client confidentiality and will do the same for you. If y…
I also had email account specific to each client, so that I could have a mail program on that ThinkPad access only the respective account.
There are many reasons to do one laptop per client (especially if you're WFH, not traveling), including not exposing personal and other-client stuff to whatever weird stuff is in the build environment of one client.
Another reason, though this never came up for me, is that there can be legal orders to permit inspection of the computer, online accounts, etc., including by computer forensics. If that happened for one client, that could be in conflict with your obligations to another client (as well as in conflict with your SO's private vacation photos, if they were on the same device). Being able to reassure that everything for a client was compartmentalized to certain devices and accounts might come in handy.
At one point, I even had color-coded labelmaker tape to help keep track of what was compartmentalized to what. And photos of the devices with the physical labeling on them, in case I ever needed to convey that I took it seriously.
(Related: One time, I had a hard drive fail such that (despite encryption) I couldn't do an approved wipe of it before disposal or warranty return. That client's compliance policies required that I physically destroy the drive platters, and ship the remnants to them via Registered Mail. It was a slightly fun/cool exercise, especially since the platters shattered nicely. And the neighborhood of $100 lost was well-invested in professionalism goodwill with a client who paid a few orders of magnitude of that amount over time.)
(In some ways, I'm now happy to no longer be running a consulting business, mainly because a predictable, consistent amount of money just appears in my bank account every couple weeks. :)