In terms of the actual role such tech can play in a campaign, this can be broken down into a few categories:
1: Set Dressing
This is the main purpose of the more low-level clockwork tech. Mentioning a military officer consulting his pocket watch, or a servant scurrying around a merchant's garden to wind up all the clockwork songbirds sitting in the trees, is a great way to efficiently communicate the wealth and sophistication of the setting. It also serves as a good way to remind players that this isn't just Generic Fantasyland, keeping everything sharp and vivid and strange. If the PCs then go on to find a way to turn the watch or the clockwork songbirds to their advantage, then so much the better!
2: A Resource for Players
Much of the low- to mid-level technology has obvious uses to PCs. A small yaga makes a great mobile base of operations; a peppergrinder gun is a good weapon for a technologically-minded character, and a set of clockwork wings makes it possible for PCs to reach and explore places that might otherwise be entirely inaccessible. There's no reason to be stingy about allowing PCs access to this sort of technology, and its existence will, again, help their adventures to stand out a little from the normal sub-medieval fantasy which D&D usually defaults to.
3: A Chance for Scholars to Show Off
Being the Guy Who Knows Stuff is great, but it can also be pretty passive; you encounter something, the GM tells you what you know about it, you relay that knowledge to the rest of the party. Of course, a clever scholar will find plenty of more active ways to employ their knowledge, but being clever all the time is hard work. Tech ratings give scholars an obvious way to get stuck into the action: reprogramming clockwork robots, reactivating ancient mechanical defence systems, piloting weird clockwork vehicles, and so on. It gives them an excuse to be front-and-centre, rather than just hiding at the back wishing they'd stayed at university...
4: A Source of Mindless Enemies
Due to its romantic fantasy leanings, ATWC is pretty short on Designated Baddies who exist only so that the PCs can butcher them. Pretty much no-one in the setting (except, maybe, the Wicked King) is Just Plain Evil; even the maddest and cruellest inhabitants of the Wicked City are more victims of their environment than anything else. Sometimes, though, even the most philosophical of gaming groups are going to just want to hit something: and even the most morally scrupulous PCs probably won't get too upset about smashing up waves of mindless wind-up clockwork soldiers.
5: A Source of 'Puzzle' Encounters
High-level clockwork tech is very powerful, but also very limited. Putting the PCs up against enemies in Steam Knight armour, or a mech, or a tank, can thus make for a great encounter: brute force approaches are likely to fail horribly, but there are lots of ways for PCs to play on the weaknesses of their enemies and come out feeling very pleased with themselves indeed. Mechs can be tripped; Steam Knights can be overheated; tanks can be lured into difficult terrain, or simply evaded until their springs run down. The best thing about these sorts of victories is that they're legitimate: they're a logical result of the limitations of the technology itself, rather a matter of the GM painting some kind of artificial 'weak spot' on the enemy and then winking meaningfully at the players until they work out to start hitting it there for massive damage. All you need to do is mention how slow this seemingly invincible death-machine is, how clumsy, how ponderous, how desperately close to overheating, and the PCs will be able to work the rest out for themselves. And then steal it from their defeated enemies.
Which leads to...
6: A Chance For the PCs to Drive Around in a Fucking Tank
Or a mech. Or a huge fuck-off Yaga with a cannon on the roof. There's no need to worry about this being 'overpowered': such vehicles can't be taken into cities, dungeons, or even the rougher sort of wilderness, and they eat so much coal that they're never going to be a really practical long-term choice of transportation technology. But for a while, before they have to abandon it because you can't drive a tank up a mountain or because the Lost City of the Dead is woefully short on places to refuel your giant mech, they're going to feel absolutely awesome - especially when they drive it back to that huge monster they had to run away from earlier and shoot it to bits with swivel guns. Indulge them in this, and the tank will soon be a beloved member of the party, embroiling the PCs in all kinds of further adventures and complications...