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.

Since then, his Iron Spider design, or variations of it ... remembered to include built-in web shooters. The first appearance of Peter using webs is in Ultimate Spider-Man (2024) #2 by Hickman ...