Manby, who rose to prominence with a last-16 appearance on his World Darts Championship debut, was well-fancied to claim his Tour Card at the UK Q-School in Milton Keynes.
The 20-year-old saw off veterans Steve Beaton and Mervyn King and a second-round rally from Matthew Dennant en route.
Samuel Price was the winner of the eighth and final Tour Card in the UK, securing himself a place on the circuit for the first time.
At the European Q-School in Kalkar, Germany, former World Matchplay semi-finalist De Zwaan got himself back on the PDC Tour after recording wins against the likes of Andreas Harrysson and Alexander Merkx.
De Zwaan's Dutch compatriot Lap earned his first-ever Tour Card with key victories over Teemu Harju and Jurjen van der Velde.
A further 13 Tour Cards were handed out across both Q-Schools to players via their respective Ranking Lists.
Five of those were distributed in the UK, with seven-time major finalist King picking up one with a second-place finish behind Stephen Burton.
The remaining Tour Cards went to England's Tyler Thorpe, Ireland's Stephen Rosney and Scotland's David Sharp.
Several big names missed out on a Tour Card, however, including the likes of Fallon Sherrock, Harrysson, Beaton and Jose de Sousa.
Sherrock suffered a fourth straight first-round defeat, meaning Beau Greaves will be the only female player on the PDC circuit in 2026.
Sweden's breakout World Darts Championship star Harrysson was denied via legs difference, while former Grand Slam winner De Sousa exited at the quarter-final stage.