Usually yes. A school, office or hotel network can log that you connected to anyproxy.site and its regional servers. Managed devices with TLS inspection may see the pages too, and your browser history keeps the real site address.
Full answer
This is about networks and devices someone else runs: school Wi-Fi, an office network, a work laptop or a hotel. Any of them can see that you connected to AnyProxy. The regional servers that carry proxied pages, such as sg.anyproxy.site, show their name in the connection setup, so a firewall or filter can log it even though the pages are encrypted. Many filtering products have a proxy or anonymiser category and block such sites outright. On a managed device it can go further. If the organisation installed its own root certificate for TLS inspection, it can decrypt and read the pages themselves. The device also keeps a local trail: through AnyProxy a page's address looks like sg.anyproxy.site/_o/ followed by the real site address in base64, and some addresses end with the real link in plain text, so browser history shows where you went to anyone who checks the device. A private window avoids the history, not the network logs. Whatever the network can see, its acceptable-use policy applies to you, and many school and workplace policies forbid proxies specifically.
In practice
Three layers. The network logs connections, including the proxy's regional server names. A managed device with TLS inspection may read the pages. And the browser stores proxied addresses that carry the real site address, encoded or in plain text. Only the history is in your hands.
Sources: Google - Allow or block access to websites (Chrome Enterprise and Education) · MITM - glossary · Can my ISP see I used a proxy?
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