I know that a VPS provider can track the client connected to a VPS (This Q/A) using RDP(Remote desktop protocol). But my question is about websites accessed from the VPS using a browser. Can they know anything about the main client (IP/Location/Local Time etc.) behind the RDP through the browser http (or https or any) protocols?
They can't track you via RDP. that only makes sense for servers you connect to using RDP.
Websites will usually see the IP address of the VPS, but browsers are very leaky when it comes to user data: for example, WebRTC tends to leak your local IP address.
Your browser will probably leak the language of your system. Not many places that speak Farsi…
local time is often delivered indirectly via time zone information, and can often be inherently a part of the connection buildup.
Location: usually your browser will ask you before it shares that explicitly.
Also: honestly, when I use my VPS to connect to the internet when I'm using a hotel Wifi, I get Google in Arabic. Which means that of the servers hosted by that hoster, the majority of people using a VPS to surf have an Arabic account or at least browser, and Google has decided that the whole address range belongs to some Arabic uplink. I don't care – it certainly is refreshing at times. But the illusion that "nobody knows you're an Iranian when using the same VPSes as a lot of other Iranians" simply doesn't hold.
And: tracking cookies are a pervasive thing. If you use any large website without an ad blocker, the ad networks can track you as singular user. Obviously, same for being logged in to facebook, twitter, instagram, pinterest, …. The info is way more relevant than your IP address (often, hundreds to millions of people share the same IP address – for example, many internet service providers to carrier-grade NAT), because it allows tracking of a user as individual, across multiple sites. The ad-network acts as aggregator here. Where one website could at worst see that your computer accessed it at some point, the ads that are embedded on many sites allow them to cross-link where you've been. That's why you see ads for the same things you tend to like on a different page.