I’ve got a similar setup to yours and after a lot of thought and some bad Amazon purchases, I settled on a KVM switch.

My personal laptop is used for work as I remote into another machine. That allows me to have my email and other personal things open while I work off the other two monitors. I switch to my work laptop when I need to use work specific resources.

This may sound odd but I remote into my customer’s network, and use my work laptop for my employer’s resources.

I settled on a $100 KVM switch from Amazon (link and it does a great job.