IP address is the same

Yes this is possible. You need to set up your own router/exit node and route traffic through it. See this knowledgebase article:

https://zerotier.atlassian.net/wiki/spaces/SD/pages/7110693/Overriding+Default+Route+Full+Tunnel+Mode

You’d have to own a block of IPv4 & IPv6 addresses and assign addresses from that range to do this, otherwise it would show the IP address of your router/exit node.

We do not operate any routers/exit nodes for “Privacy” style VPNs.