There's nothing in the mechanism of a hammer drill preventing it to turn in both directions, although the hammer action is meant to be used with the "screwing" direction.
If you buy a combi drill that's meant to screw screws, it will have forward and reverse, otherwise it would be useless for unscrewing. You can always check for presence of the direction switch on the product photos.
That said, hammer drills are useless at most things except making a lot of noise. Hell, I have a Makita DHP486 which is a monster, and the hammer drill on it is useless, as expected.
There's a contradiction in your requirements: for light screwing, you need a small lightweight driver that is short enough to fit where it needs to go inside furniture and cabinets, and it has to be usable with one hand in awkward positions. It needs good trigger speed and torque control, so you can set the screw flush with the workpiece without over-driving it into the board.
For hammer drilling, nothing beats a SDS drill. But if you want a combi drill that does both, it'll have the useless hammer action, and it will also be large and heavy. So it will be less practical for the stuff you actually use it the most for.
So instead, I'd say keep the corded hammer drill to make holes in bricks, and get a nice, small, lightweight driver-drill without hammer action. For example this one:
It's the smallest 18V brushless from Makita. I have big hands, but still, it's tiny. It will screw screws larger than itself into 5" thick wood, and it also has a very accurate trigger, so the small screws .
So basically, don't get the big drill just because you'll drill into brick twice a year. Dust off your corded one for that, and instead get a small light drill, 14V or 18V. I got the small battery instead of the big one, because it is lighter, and if you have two batteries instead of one, you can have a battery in the charger. With the 2-speed gearbox, you get a nice combination of speed and torque.
Especially, don't buy a big drill like the Makita DHP486 if you want to do furniture. It's for the big lag bolts. It has so much torque it will throw you off the ladder if you're not careful. It's just ridiculous.
As for brand, don't listen to the fanboys, between Makita Dewalt Milwaukee there's no winner, they're all top-notch. Also too expensive for occasional use, unless you get a very good deal. I've renovated a few condos and built a house with a pair of €30 LIDL cordless drills, that also works, but of course it's less... luxurious, and after an encounter with a stubborn piece of wood, one of them just burned. So that was definitely too cheap. Problem with cheap brands also is they change models often and come up with new batteries (or go out of business) so when the battery dies you have to buy a new drill. So I'd recommend mid-range brands instead.
A good test is to see if you can put in a 1" screw into particle board in second gear, and have it perfectly flush without overdriving it.