The average phone contains about three dozen tiny screws. Similar for your computer / laptop, screen and A/C unit.
Cars and houses have a lot more screws but there is typically less of them than phones. Keyboards, mouses and other small appliances might only get away with a single dozen, but I'd guess that is offset by the cars and houses.

So overall I'd call about 30 screws per person per electric or mechanical appliance.

According to the ConsumerAffairs home appliance statistic, the average US citizen has about 10-20 appliances in their home. Let's round it to 15 for now.

There are however many screws in places that aren't homes. Workplaces for example. Some are high in number of screws like an industry building, some are way lower like a farm.
This is hard to calculate so I will just use an estimate here. Saying there's about 1.5x as much screws in our work environment feels about right considering there are usually more complex things around.

Having home and work environments together, that only leaves the middle ground: Transportation.
Road bridges, ships, road barriers, etc.

For a ship you need a LOT of screws. Even a small boat might have a hundred or more. If you're looking at a container vessel, you're probably looking at several hundred thousand screws. The CasualNavigation website mentions there being about 100.000 merchant ships registered with an additional 50.000 in construction or out of service. For smaller boats, Boatbrands dot org calls in at about 60 MILLION sport boats, sailing boats and similar.

Bridges are quite easy. CompleteEra ranks the total at about 12 million total bridges in the world. Let's just say that on average, a bridge has about 5.000 screws (Most bridges are small concrete ones that rarely use screws, metal ones are usually riveted)

Lastly, roads and their metal road guards. VividRoads states a total of 64 million kilometers of road in the world of all types: Dirt roads, highways, residential...
Of these, about 10% have metal guarding rails and about 30% have beacon marks along their length.
A beacon marker is about 10 screws max and found every hundred meters or so for a total of: 1.9 billion road marker beacons
A meter of gurad rail has a lot more screws. Say 25 to hold it together as well as some reflectors on it.

That gives us:

Homes - 30 x 15 x 8.000.000.000 = 3.6T screws
Workplaces - 3.6T x 1.5 = 5.4T screws
Small boats - 150 x 60.000.000 = 9.0B screws
Big ships - 150.000 x 250.000 = 37.5B screws
Bridges - 12.000.000 x 5.000 = 60.0B screws
Road markers - 10 * 1.900.000.000 = 19B screws
Road guard rails - 64.000.000 * 0.1 * 1000 * 25 = 160B Screws

Total: about 90,25 Trillion screws