I don't understand how my question is off-topic. It talks about a desktop app, called Steam browser.
I think "off-topic" wasn't the right reason for closing it. But in essence, your question just can't be answered in its current form. Let me explain why I think so.
Why the question doesn't make sense
I was buying a game and the Paypal page opened inside Steam browser. I fear they could sniff password. Is there any proof that they don't?
That's not making much sense from a logical standpoint. You are trying to falsify your claim that they apparently sniff your passwords. In order to get the proof that nothing is sniffing your password, you need to make sure that all of the below components are safe.
- Your computer hardware
- Your operating system
- The Steam client
- The Browser plugin
- The HTTP(S) connection
- The PayPal side
You would have to inspect all of these. You would need to have the source code for Steam. Does that seem doable? Not to me. Can you be 100% sure? Never.
Why I'd have closed it
What would you have expected as possible answers? How should a good answer look like? The only definitive answer I can think of is:
I work for Steam and I can tell you, we don't sniff passwords!
Then again… would you trust that? But every other answer would include speculation. This falls into the definition of "not constructive":
We expect answers to generally involve facts, references, or specific expertise; this question will likely solicit opinion, debate, arguments, polling, or extended discussion.
Moreover, don't you think that if there was any concern about safety, some people would have complained? PayPal fraud is quite common, and a big business like Steam couldn't afford to have security issues there.