When I try to open modpack, the launcher screen does not appear. I've tried a few different launchers besides curseforge, but they all have the same problem

This is most likely related to firewall or antivirus. Try to remove File Director mod, or just remove this file https://github.com/Krutoy242/Enigmatica2Expert-Extended/blob/master/config/mod-director/optifine.url.json

Its work thanks for helps