Archive of Our Own is basically the central hub these days. It's got the tagging system, so you can filter for 'Love Live! School idol project' and then sort by update date to see what's freshly posted. The quality varies wildly, but the sheer volume means there's always something new, and the kudos/bookmark system surfaces decent stuff eventually.
Tumblr still has a niche for shorter, character-study pieces and rarepair content that might not get full fics on AO3. You have to follow specific blogs or search tags like '#lovelivefanfic' though; it's more of a curated, social experience than a repository. I found some amazing EliUmi micro-fics there that never migrated anywhere else.
Wattpad hosts a different demographic, often younger writers doing reader-inserts or high-school AUs. The update notifications are aggressive, so if you follow a story, you'll know. The search is terrible, so I'd only go there if a specific author you like cross-posts. The comment sections are… vibrant, let's say.
FanFiction.net is the old guard. Some long-running epics from the peak Sunshine!! era are still getting sporadic chapters there. The interface is clunky, but sorting by update date still works. You'll miss a lot of newer, queer-themed work, though, as the culture shifted to AO3 for that. It's worth a glance for completed classics, but not the first stop for fresh material.
Discord servers are the hidden layer. Many fanfic writers have private servers where they share drafts, snippets, and exclusive one-shots. You usually find links to these on their AO3 profiles or Tumblr. It's less about browsing and more about community access; the updates feel immediate and the discussions can influence where the story goes next.