With 47 employed and 24 unemployed NPCs (not counting 9 kids/students and 4 retirees), Disco Elysium's unemployment rate is 33%, or one third.
I only counted characters who we encounter in Martinaise at the time of the game's events, independent of where they are employed or live.
Employed characters:
Dockworker's Union:
Evrart Claire: Dockworker union leader
Titus: Dockworker / Hardie boy
Alain: Dockworker / Hardie boy
Eugene: Dockworker / Hardie boy
Fat Angus: Dockworker / Hardie boy
Glen: Dockworker / Hardie boy
Shanky: Dockworker / Hardie boy
Theo: Dockworker / Hardie boy
Santiago: Dockworker
Elizabeth Beaufort: Union lawyer
Ruby: Works for the Dockworker's Union
Easy Leo: Dockworker
Call me Manana: Dockworker
Measurehead: Dockworker's Union Security
Lorry drivers:
Paledriver: Lorry Driver
Racist Lorry Driver: Lorry Driver
Sileng: Lorry Driver and street vendor
Tommy Le Homme: Lorry Driver, aspiring musician
Mercenaries:
Phillis de Paile: Mercenary
Raul Kortenaer: Mercenary
Ruud Hoenkloewen: Mercenary
RCM:
Harry: Employed, RCM officer
Kim: Employed, RCM officer
Jean Vicquemare: Employed, RCM officer
Judit Minot: Employed, RCM officer
Trant Heidelstam: RCM consultant
Other employed characters:
Billie Méjean (Working Class Woman): Employed, unclear where (but it's in the name)
Bird's Nest Roy: Runs a pawn shop
Charles Villedrouin (Sunday Friend): Moralintern buerocrat
Cleaning Lady: Cleaner
Frittte clerk: Clerk / cashier
Gary the Cryptofascist: Cake deliverer
Gorący Kubek: Cook
Joyce Messier: Wild Pines representative
Lawrence Garte: Cafeteria Manager / Bartender
Lilienne: Fisherwoman
Marielle Charpentier: Real estate agent
Man behind the "Mysterious Pair of Eyes" - likely working for the Dockworker's Union as a spy
Novelty Dicemaker: Dicemaker
Plaisance: Book store owner
Washerwoman: Washerwoman
Smoker on the Balcony: Sex worker
Elena (Coalition Warship Archer's signaller): Employed, Moralintern signaller
2 Waterlock workers
Unemployed characters:
Ravers:
Egghead: Unemployed - but either becomes a DJ or helps with the drug lab)
Acele: Unemployed - but helps with a drug lab / nightclub
Andre: Unemployed (but helps with a drug lab / nightclub
Noid: Unemployed (but helps with a drug lab / nightclub)
Other unemployed characters:
Cindy the Skull: Unemployed, even though Harry can give her a job in the ultraliberal questline
Idiot Doom Spiral: Unemployed, even though Harry can give him a job in the ultraliberal questline
Don't Call Abigail: Unemployed
Rosemary: Unemployed
Klaasje Amandou: Unemployed - former industrial spy
Mega Rich Light-Bending Guy: "Investor", but that is not a job in the formal sense
Soona: Former programmer at Fortress Accident
Sylvie Malaiika: Former bartender, quit her job
The Deserter: His bosses are long gone
The Pigs: Only employed in her fantasy
Uuno de Ruyter: Cuno's dad, in the process of dying
Unclear, but lingering around at working hours, thus counted as unemployed:
Pissf***ot: Juvenile delinquent
Fuck the World: Juvenile delinquent
Random Drunk
Bald guy in the Whirling
Measurehead's Babe 1
Measurehead's Babe 2
Measurehead's Babe 3
TL;DR: 47 employed, 24 unemployed, 33.8% unemployment.