In Avengers: Infinity War, it's shown that the MCU Peter's web-shooters can, like Iron Man's armor, self-assemble when activated. Strangely, not every version of Spider-Man uses web-shooters.

Spider-Man's upgraded Web-Shooter 2.0 adds a weaponized twist to his classic gadget, designed by Peter himself. A mind-swapping machine brings out an alternate Peter Parker with advanced gadget ...