Maybe one could argue that Bilbo has 'spun' Gandalf's role in TH to make
him seem responsible for a respectable Hobbit going off into the wild & having adventures
I do think that the Gandalf of TH is different to the Gandalf of LotR (or of The Sil for that matter). Perhaps this is due to Tolkien's changing of the character as the Legendarium developed. Certainly, in TH Gandalf is more of a typical 'wizard', & often a deus ex machina. I think a comparison between the way he's played in the BBC radio adaptations of
The Hobbit & LotR & the movies shows up the difference clearly. The way Heron Carvic plays him in The Hobbit captures the Gandalf of the book perfectly, sharp, mercurial, affectionate but exasperated, in love with his own cleverness. This Gandalf would not have worked in LotR but is right for TH.
Wish I could find a clip of Carvic's Gandalf to make the point clearer, but I think, in answer to your question, Gandalf does manipulate others - he is a 'steward' & has responsibilities, & perhaps sometimes takes 'short cuts', but then he is out to try & save the world, often having to get aid from those who are too caught up in themselves. His heart is in the right place, but I wonder whether his horrified response on being offered the Ring by Frodo might have had something to do with a realisation of this tendency in himself?