MTB/Gravel tires for a Cannondale Bad Boy 3

Hello there,
And of course I hope this is the right cat for the post. I would need a slight help with the choice of tyres for my Bad Boy (which is a 650b hybrid) from Cannondale currently on Schwalbe Kojak 650b x 1.35” slicks. This is great for the town but even a slight puddle with mud is dangerous on these so I would like something that has atleast slight tread. The more expensive models of the Bad Boy come with Scwalbe G-One 650b x 1.5” gravel tyres on the same 25c rim I believe. Atleast thats what I was told, that the 25crim Im on is capable of running up to 40c/1.5” tyres. My question is, is this really the case? Theres loads of clearance, even for a 2” tyre probably, but there are not many options. Can someone recommend some? And maybe explain more on what is safe to run on these rims? Im not looking to convert this bike to a hardtail mtb but most of commuting and riding is XC with gravel and muddy grass roads.