Move integer-like primary key normalization to `new_column_definition`

Currently the normalization only exists in `primary_key` shorthand. It
should be moved to `new_column_definition` to also affect to
`add_column` with primary key.

activerecord/lib/active_record/connection_adapters/abstract/schema_definitions.rb

@@ -410,6 +410,10 @@ def create_column_definition(name, type, options)
         def aliased_types(name, fallback)
           "timestamp" == name ? :datetime : fallback
         end
+
+        def integer_like_primary_key?(type, options)
+          options[:primary_key] && [:integer, :bigint].include?(type) && !options.key?(:default)
+        end
     end
 
     class AlterTable # :nodoc:

activerecord/lib/active_record/connection_adapters/mysql/schema_definitions.rb

@@ -4,11 +4,6 @@ module ActiveRecord
   module ConnectionAdapters
     module MySQL
       module ColumnMethods
-        def primary_key(name, type = :primary_key, **options)
-          options[:auto_increment] = true if [:integer, :bigint].include?(type) && !options.key?(:default)
-          super
-        end
-
         def blob(*args, **options)
           args.each { |name| column(name, :blob, options) }
         end
@@ -62,6 +57,10 @@ class TableDefinition < ActiveRecord::ConnectionAdapters::TableDefinition
         include ColumnMethods
 
         def new_column_definition(name, type, **options) # :nodoc:
+          if integer_like_primary_key?(type, options)
+            options[:auto_increment] = true
+          end
+
           case type
           when :virtual
             type = options[:type]

activerecord/lib/active_record/connection_adapters/postgresql/schema_definitions.rb

@@ -44,15 +44,8 @@ module ColumnMethods
         # a record (as primary keys cannot be +nil+). This might be done via the
         # +SecureRandom.uuid+ method and a +before_save+ callback, for instance.
         def primary_key(name, type = :primary_key, **options)
-          options[:auto_increment] = true if [:integer, :bigint].include?(type) && !options.key?(:default)
           if type == :uuid
             options[:default] = options.fetch(:default, "gen_random_uuid()")
-          elsif options.delete(:auto_increment) == true && %i(integer bigint).include?(type)
-            type = if type == :bigint || options[:limit] == 8
-              :bigserial
-            else
-              :serial
-            end
           end
 
           super
@@ -185,6 +178,18 @@ def xml(*args, **options)
 
       class TableDefinition < ActiveRecord::ConnectionAdapters::TableDefinition
         include ColumnMethods
+
+        def new_column_definition(name, type, **options) # :nodoc:
+          if integer_like_primary_key?(type, options)
+            type = if type == :bigint || options[:limit] == 8
+              :bigserial
+            else
+              :serial
+            end
+          end
+
+          super
+        end
       end
 
       class Table < ActiveRecord::ConnectionAdapters::Table

activerecord/lib/active_record/connection_adapters/sqlite3/schema_definitions.rb

@@ -3,27 +3,19 @@
 module ActiveRecord
   module ConnectionAdapters
     module SQLite3
-      module ColumnMethods
-        def primary_key(name, type = :primary_key, **options)
-          if %i(integer bigint).include?(type) && (options.delete(:auto_increment) == true || !options.key?(:default))
-            type = :primary_key
-          end
-
-          super
-        end
-      end
-
       class TableDefinition < ActiveRecord::ConnectionAdapters::TableDefinition
-        include ColumnMethods
-
         def references(*args, **options)
           super(*args, type: :integer, **options)
         end
         alias :belongs_to :references
-      end
 
-      class Table < ActiveRecord::ConnectionAdapters::Table
-        include ColumnMethods
+        def new_column_definition(name, type, **options) # :nodoc:
+          if integer_like_primary_key?(type, options)
+            type = :primary_key
+          end
+
+          super
+        end
       end
     end
   end

activerecord/lib/active_record/connection_adapters/sqlite3/schema_statements.rb

@@ -39,10 +39,6 @@ def indexes(table_name, name = nil)
           end
         end
 
-        def update_table_definition(table_name, base)
-          SQLite3::Table.new(table_name, base)
-        end
-
         def create_schema_dumper(options)
           SQLite3::SchemaDumper.create(self, options)
         end

activerecord/lib/active_record/migration/compatibility.rb

@@ -93,13 +93,7 @@ class << t
 
         def add_column(table_name, column_name, type, options = {})
           if type == :primary_key
-            case adapter_name
-            when "PostgreSQL"
-              type = :serial
-            when "Mysql2"
-              type = :integer
-              options[:auto_increment] = true
-            end
+            type = :integer
             options[:primary_key] = true
           end
           super