Based on the specs listed on your link to your bike, your Left shifter is a 2x only, meaning it will only work with a double front crankset. There is a 3x version of this shifter (M315). Your Shimano front derailleur is what is termed a "double front derailleur" meaning it is designed to work with the 2x crankset. While there are hacks that can enable a double front der to work on a triple chainring crankset (aka 3x), it is limited by the fact it is designed for a max large chainring of 36 teeth. Using it with a larger crankset-- especially a 3x-- will yield shifting problems and chain rub: read frustrating and annoying. With these two facts alone, one can ascertain that if a larger gear ratio is desired, more than just changing the crankset will have to happen.
Regarding the crankset, the chainrings are riveted and thus, cannot be replaced individually. Your proposed Shimano upgrade to FC-M315 doesn't do anything for increasing your gear ratio, as the 2x version is a 36-22 tooth count as well, and these chainrings are also riveted. Your bike has a square taper bottom bracket (the bearing assembly that the crankset fits on to) with a spindle length of 123mm. This is significant because any crankset you switch to must also be a square taper and have a reasonable chainline when on a 123mm spindle (in order to keep your current bottom bracket. You can put a good many cranksets on your bike as long as you also have or install a compatible bottom bracket).
All said, upgrading to a higher gear ratio will involve more than a change of chainrings. At least a different front derailleur for sure and possibly a different front shifter if you go to 3x up front. Regarding the "speed" listed for your crankset (7/8 speed) and any potential replacements: you can utilize a 9 speed crankset within your current set up and retain the same quality of performance as 7/8 speed (the above noted hurdles still exist, but being "9 speed" wouldn't really be an additional one).
While writing this I referred a few times to Shimano's latest Specification and technical document which outlines several details of their current lines of componentry. I noted a listing for a crankset, model FC-TY501-2, which is a double chainring crankset sporting 46 & 30 tooth rings and fits on to a square taper spindle 123mm in length. IF clearance isn't a problem with the larger chainrings, this would be a viable option for you as you could retain your current 2x shifter. You would need a more capable front derailleur (although I would certainly determine how unhappy the current FD became with the larger rings before installing a properly spec'd one). At any rate, front derailleur's are being heavily discounted at many retailers (especially online) as demand for them plummets with the rise of the 1x systems. If all that is required to successfully raise your gear ratios on that bike is a larger crankset and a different front der, that is about as good as you can do from an economical and ease of installation standpoint.