Fix installing from API with tap names

Library/Homebrew/api/bottle.rb

@@ -22,6 +22,7 @@ module Homebrew
 
         sig { params(name: String).returns(Hash) }
         def fetch(name)
+          name = name.sub(%r{^homebrew/core/}, "")
           Homebrew::API.fetch "#{bottle_api_path}/#{name}.json"
         end
 
@@ -85,7 +86,9 @@ module Homebrew
 
           # Map the name of this formula to the local bottle path to allow the
           # formula to be loaded by passing just the name to `Formulary::factory`.
-          Formulary.map_formula_name_to_local_bottle_path hash["name"], resource.downloader.cached_location
+          [hash["name"], "homebrew/core/#{hash["name"]}"].each do |name|
+            Formulary.map_formula_name_to_local_bottle_path name, resource.downloader.cached_location
+          end
         end
       end
     end

Library/Homebrew/api/cask-source.rb

@@ -12,6 +12,7 @@ module Homebrew
 
         sig { params(token: String).returns(Hash) }
         def fetch(token)
+          token = token.sub(%r{^homebrew/cask/}, "")
           Homebrew::API.fetch "cask-source/#{token}.rb", json: false
         end
 

Library/Homebrew/cmd/install.rb

@@ -138,11 +138,12 @@ module Homebrew
     end
 
     args.named.each do |name|
-      next if EnvConfig.install_from_api?
       next if File.exist?(name)
-      next if name !~ HOMEBREW_TAP_FORMULA_REGEX && name !~ HOMEBREW_CASK_TAP_CASK_REGEX
+      next unless name =~ HOMEBREW_TAP_FORMULA_REGEX
 
       tap = Tap.fetch(Regexp.last_match(1), Regexp.last_match(2))
+      next if (tap.core_tap? || tap == "homebrew/cask") && EnvConfig.install_from_api?
+
       tap.install unless tap.installed?
     end