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You can use a third party wallet like Vessel or SteemConnect.

Vessel ?

Is there something like Scatter EOS for Steem?

There are Vessel and SteemConnect. They aren't exactly the same, but they serve similar purposes.

SteemConnect is centralized , Vessel is nice but it doesn't interact with web pages. Scatter extension and desktop are cool because you can autenticate and transact without storing the password in the browser or 3rd part services

Vessel does support that, but it is not used in many places.