While attached to a web, pull back sharply with your hand to fling yourself forward.
This is the gold standard for web-slinging. It adds physics-based swinging, web-zipping, and air control. You can find it on SpiderLab - Thunderstore .
To look the part, download high-quality models ranging from the classic Raimi suit to the Miles Morales "Spider-Verse" look. Many are available on Spider-Man Avatar Pack - Mod.io .
Once installed, the mod grants specific gesture-based powers:
Simply grab onto any surface; the mod allows you to "stick" and climb most textures.
You typically need MelonLoader, BoneLib , and AudioImportLib for advanced code mods like SpiderLab.