At the end of No Way Home Peter shows up with the new suit and looks like he's sewn it on. Why doesn't he use a stark designed suit just like the homecoming suit, the far from home or nano tech iron-spider suit armor or the hybrid suit we see at the end of the movie.
Peter Parker's identity was taken out of existence in No Way Home and that's the main reason he can't wear those suits. The suit hasn't disappeared because people have forgotten who's under the mask but not Spider-man who wears his suit to avoid his identity.
Peter can use those suits before No Way Home because his bio-metric identity was uploaded to the software of the suits designed by Stark. His identity was removed from the whole universe, So his bio metric identity was also removed from the suits software. That's why he can't use any of his suits and the technologies he has.
He sews his new suit himself and looking at the new suit it seems that it is more comical. There is no Stark technology in it, MCU Spider-man has always been criticized because it uses Stark technology. Now the time has come that he will fight his journey alone.
The upcoming Spider-Man movie will have a comic occult story line and some fans are speculating that the villains of Spider-Man 4 will be Scorpion and Venom. Marvel confirms that Spider-Man 4 will not be epic like No Way Home.