It's at least plausible that, at least originally, defeating Clinton wasn't a goal, weakening and dividing the US as a whole and the expected next President’s public and Congressional support might have been the whole goal. Actually causing her defeat may be a happy accident from the Russian POV (or a bit of a unhappy one that required escalating efforts to promote disunity, because in the short-term, even if the administration produced was not particularly popular, there was the risk of accidental strength from executive-legislative partisan alignment.)
Well, there is the Steele dossier, which FusionGPS was paid twice for - once by a Republican PAC, then second by Clinton's Perkins & Coie - before providing it to the FBI directly. You could say that it's MI5/MI6 (once a <three letter agency> operative, always a <three letter agency> operative, amirite?) intel, but the unverified parts of it are from Russian sources.
The investigation into Trump's campaign and its Russian contacts was NOT started by the dossier. The FBI was not given the dossier until December of 2016. By this time there was no campaign anymore since Trump was president-elect. In fact the investigation had already started months prior when Papadopolous made suspicious comments to a diplomat about the campaign's knowledge of information related to Hillary's emails. [2]
[1] https://www.wired.com/story/why-trump-wont-stop-talking-abou... [2] https://en.wikipedia.org/wiki/Trump–Russia_dossier
But October 2016 is still after Page left the Trump campaign, and after the Russian investigation had started.