First off, Rift is for 'Rift mods' I have a thread listing compatible Rift mods so any new mods that come up 90% of them are Forge 1.13.2 supported basically. Go visit that to know what is Rift compatible and what I now update that thread with it Forge 1.13.2 mods these days since few updates come to Rift mods these days, the odd time but less and less updates to almost none now with Forge 1.13.2 happening and people moving to it. And any open to 1.14 are moving to Fabric.
Rift Discussion Thread, for anything to tell you the difference between Rift and 1.13.2 Forge and updated daily for fans by a fan that wanted to know the answer one day. :)
Created this midway through Rift relevance and before 1.13.2 Forge was a thing and to cover Rift mods despite the '1.13. Forge where is it?' phase and video clickbaiting going on youtube before 1.13.2 Forge came out. So I know what's been going on even for covering Rift and I'm not part of their team I'm just player/mod content fan that informs about it as best I can.
Secondly, I'd recommend 1.12.2, Forge 1.13.2 is not ready yet, it might be open to the public, but for a public beta period it isn't ready for modpacks or anything. I've tested a few of the mods any chance I get in-between Fabric mod testing and updates and Forge 1.13.2 mods or Forge itself is functional somewhat but not ready yet. You try and notice mod developers making adjustments or easing in their blocks, recipes and so on. You can tell from that even if you don't see the coding, but the content/updates show for Forge mods being ported to 1.13.2 over time. Only use 1.13.2 Forge unless you wish to test mods and report to developers or the Forge team, otherwise don't bother.
Twitch & Forge I've answered in another thread. In short Forge and Twitch aren't 1.13.2 ready yet. I've tried a few times when it was possible with version 44 of 1.13.2 Forge and it won't work and gives you a Vanilla setup for profiles, I asked others who would try to work out the issues with this and they don't know either. I can't get an unofficial setup working either so it's not ready yet by any stretch, not even a 1.13.2 Forge profile would show up any time I tried to get it working. It's not ready yet. Twitch removed it as they probably know it's not ready yet but is for public beta testing. Which Twitch isn't allowing Forge states that are for public beta testing clearly which makes sense. It's why MultiMC isn't allowing 1.13.2 Forge instances yet and why Twitch removed access to Forge 1.13.2 versions because it's not ready yet for public modpack/survival or anything yet. It's public beta status, not just on the title screen when the game loads with 1.13.2 Forge properly but it shows in state/stability of Forge and mods development stages.
I wish they would allow Rift but there is a situational reason why I assume hence it isn't available. Liteloader I feel could official/unofficially but eh that's obviously 1.12.2 and not 1.13+ related.