users have tried to use usernames directly

app/models/mastodon_app.rb

@@ -103,8 +103,13 @@ def self.find_or_register(instance_name)
     app
   end
 
+  # user may input hostname (foo.social), url (https://foo.social/@user), or user (@user@foo.social)
   # extract hostname from possible URL
   def self.sanitized_instance_name(instance_name)
-    instance_name.to_s.delete_prefix("https://").split("/").first
+    instance_name
+      .to_s
+      .delete_prefix("https://")
+      .split("/").first
+      .split("@").last
   end
 end

spec/models/mastodon_app_spec.rb

@@ -1,4 +1,22 @@
 # typed: false
 
+require "rails_helper"
+
 RSpec.describe MastodonApp, type: :model do
+  describe "#sanitized_instance_name" do
+    it "accepts an instance name" do
+      expect(MastodonApp.sanitized_instance_name("example.com")).to eq("example.com")
+    end
+
+    it "accepts urls" do
+      expect(MastodonApp.sanitized_instance_name("https://example.com")).to eq("example.com")
+      expect(MastodonApp.sanitized_instance_name("https://example.com/")).to eq("example.com")
+      expect(MastodonApp.sanitized_instance_name("https://example.com/@user")).to eq("example.com")
+    end
+
+    it "accepts a user id" do
+      expect(MastodonApp.sanitized_instance_name("user@example.com")).to eq("example.com")
+      expect(MastodonApp.sanitized_instance_name("@user@example.com")).to eq("example.com")
+    end
+  end
 end