They might be able to see the domain names you visit (e.g., google.com ) if they are technically savvy enough to "sniff" traffic, but this requires specialized tools.
A VPN creates an encrypted "tunnel" for your data. Even if they own the router, they will only see that you are connected to a VPN—all other traffic will be invisible. Your Bitch Neighbour
If your computer has "File and Printer Sharing" turned on, they might be able to see and access folders you’ve marked as shared. How to get them off your network They might be able to see the domain names you visit (e
Often, people leave their router's admin login as "admin/admin." Change this so the neighbor cannot log into your router settings to find your new Wi-Fi password. If your computer has "File and Printer Sharing"
How to Hide Your Internet History from WiFi Owners - Top10VPN
Most routers have a "Connected Devices" or "DHCP Client List" section. If you see a device you don't recognize (like "Linda’s iPhone"), that’s your intruder.