“No logs” on a proxy or VPN page tells you very little, and a couple of old court cases show why. In 2011 a UK web proxy and VPN service handed over a user’s records under a court order. In 2017 a US cyberstalking complaint relied on records from a VPN whose privacy policy said it kept no logs.
A service that bills per GB and handles abuse reports has to keep something, so I’d stop asking whether a provider logs. Ask which fields, for what purpose, how long, and who can demand them. A policy that names its fields is worth more than a bold claim on the landing page.
The other half is what they can see at all. Over a CONNECT tunnel with certificate checks on, a proxy sees your IP, the hostname, timing and volume. Paths, headers, passwords and page content stay inside TLS. Turn off certificate verification and that stops being true, which is why I’d never leave verify=False in a script.
Disclosure: we run a proxy service, so we keep some of those records too.

