Only if you expose it publically without auth while routing queries through your residential connection, which is not an advised configuration.
For personal use, you can run it directly on your machine or access over VPN. Queries to upstream search engines can be forwarded over proxies or VPNs as you see fit. Some work fine over tor and some can go over commercial or DIY tunnels.
To add, I have been running instance for years for family and friends. I run it behind a nginix basic auth with a config that sets a forever cookie first time you login. Really simple. Another good option is cloud flare zero trust.
A ~dozen. Several are technical and use it because it includes several private and paid engines on request.
Config is in a git repo I give access to if requested. One of the technical users modified it to keep pretty minimal logs. I guess they are trusting me to actually use that config but trust is pretty high in the group so not really an issue.
For personal use, you can run it directly on your machine or access over VPN. Queries to upstream search engines can be forwarded over proxies or VPNs as you see fit. Some work fine over tor and some can go over commercial or DIY tunnels.