The thing is most 10 speed doubles and triples come with a minimum 24t Granny ring, where 9 speed chainsets came with a 22t, 22-32 essentially provides the same bottom end gearing as 24-36 your lowest gear on a 2×9 is essentially the same as on a 2×10… you’ll gain no more climbing advantage in that respect…
Of course you have scope to go a bit higher on the bigger chainring with 10 speed, meaning you can have a slightly broader overall gearing range, and of course you gain an extra increment as you shuffle up the cassette which might smooth things out for you a bit…
What chainset are you currently using? do you actually need a whole new chainset or just a granny, Front mech and shifter?
But if its a choice between buying a whole new drivetrain or just replacing the chain cassette and rings on a 9 speed, I’d save the pennies and just replace the worn bits for now, until the shifters and mechs are really bolloxed… or you feel fit enough to go to 1×10…
9 speed spares are still readily available, keeping it going for another 12 months is more money saved and more time for shimano to roll out new products, helping reduce the privce of 10 speed when you do make the switch…