Does HTTPS also hide the URL request in most logging systems? You can always see the domain (api.example.com) but you cannot see the URL? The benefit being it hides an API key if included in the URL?
1. hides any private information anywhere in the request, URL or otherwise, API key or otherwise. Maybe you're fine if someone knows you used Bing (revealed through DNS lookups), but not what query you entered (encrypted to be decryptable only by Bing servers). An API key is obviously secret but something as oft-innocuous as search queries can also be private.
2. disallows someone on the network path from injecting extra content into the page. This can be an ISP inserting ads or tracking (mobile carriers have been playing with extra HTTP headers containing an identifier for you for advertising reasons iirc) or a local Machine-in-the-Middle attack where someone is trying to attack another website you've visited that used https.
What it doesn't hide is the DNS lookup for that domain. You still have to translate a hostname into an IP address.
This might be a concern for certain uses. But at least it's on another port and protocol and not directly related to the HTTP request itself.
> "Server Name Indication payload is not encrypted, thus the hostname of the server the client tries to connect to is visible to a passive eavesdropper."
https://en.wikipedia.org/wiki/Server_Name_Indication
So you're right, this is more aligned to the HTTP request than the DNS resolution of hostname that I mentioned. Strictly speaking, it's not part of HTTP per se (it's part of TLS), but still, it's in the same request in the most common definition, as you are saying.