It's not supposed to be supported as 1.16 is out, but is in a grace period until 1.16 gets a recommended build of Forge, which keeps getting pushed back as Mojang threaten to release 1.16.2
I recommend using Twitch only to install and manage packs but not run them, try the following:
Install the pack via Twitch
Install the version of Forge that the pack requires
Make a new "Installation" in your launcher, setting its "Minecraft Version" to the correct version of Forge for the pack and setting its "Game Directory" to the folder that Twitch installed the modpack to
Run the pack with the normal Minecraft Launcher
This log looks like a successful connection, albeit with many errors that mod devs are apparently happy to publish mods with
Did you restart your client after getting the issue?
Try deleting your build folder and
%USERPROFILE%/.gradle/caches/forge_gradle/minecraft_user_repo/net/minecraftforge/forge/forge-1.15.2-31.2.0_mapped_snapshot_20200514-1.15.1
Those messages shouldn't have anything to do with you timing out, can you provide debug.log for both client and server using one of the sites in the "Logs" section of my signature below
No you have a COMPLETELY different issue.
I recommend using Twitch to install and manage packs, but not to run them, follow the steps in the "Logs" section, "Twitch Launcher" subsection, of my signature below to run the pack without Twitch.