How a domain connection works
Connecting a domain means telling the internet that an address you own should point to the software platform. This is done through records at your domain registrar or DNS provider. Typically you add a record for a chosen subdomain, such as a clients or books prefix, and the platform issues a security certificate for it.
None of this changes your main website or your existing email. The record applies only to the specific subdomain you choose. That separation keeps the risk low, though anyone editing DNS should still take care, because a mistyped record in the wrong place can affect other services.