diff --git a/lib/active_record/connection_adapters/cockroachdb_adapter.rb b/lib/active_record/connection_adapters/cockroachdb_adapter.rb
index f70242ce..4e376531 100644
--- a/lib/active_record/connection_adapters/cockroachdb_adapter.rb
+++ b/lib/active_record/connection_adapters/cockroachdb_adapter.rb
@@ -217,16 +217,33 @@ def check_version # :nodoc:
         end
       end
 
-      def initialize(...)
+      def configure_connection(...)
         super
 
       # This rescue flow appears in new_client, but it is needed here as well
       # since Cockroach will sometimes not raise until a query is made.
+      #
+      # See https://github.com/cockroachdb/activerecord-cockroachdb-adapter/pull/337#issuecomment-2328419453
+      #
+      # The error conditions used to differ from the ones in new_client, but
+      # the reasons why are no longer relevant. We keep this in sync with new_client
+      # even though some conditions might never be checked.
+      #
+      # See https://github.com/cockroachdb/activerecord-cockroachdb-adapter/pull/229
+      #
+      # We have to rescue `ActiveRecord::StatementInvalid` instead of `::PG::Error`
+      # here as the error has already been casted (in `#with_raw_connection` as
+      # of Rails 7.2.1).
       rescue ActiveRecord::StatementInvalid => error
-        no_db_err_check1 = @connection_parameters && @connection_parameters[:dbname] && error.cause.message.include?(@connection_parameters[:dbname])
-        no_db_err_check2 = @connection_parameters && @connection_parameters[:dbname] && error.cause.message.include?("pg_type")
-        if no_db_err_check1 || no_db_err_check2
-          raise ActiveRecord::NoDatabaseError
+        conn_params = @connection_parameters
+        if conn_params && conn_params[:dbname] == "postgres"
+          raise ActiveRecord::ConnectionNotEstablished, error.message
+        elsif conn_params && conn_params[:dbname] && error.cause.message.include?(conn_params[:dbname])
+          raise ActiveRecord::NoDatabaseError.db_error(conn_params[:dbname])
+        elsif conn_params && conn_params[:user] && error.cause.message.include?(conn_params[:user])
+          raise ActiveRecord::DatabaseConnectionError.username_error(conn_params[:user])
+        elsif conn_params && conn_params[:host] && error.cause.message.include?(conn_params[:host])
+          raise ActiveRecord::DatabaseConnectionError.hostname_error(conn_params[:host])
         else
           raise ActiveRecord::ConnectionNotEstablished, error.message
         end
diff --git a/test/cases/adapters/postgresql/postgresql_adapter_test.rb b/test/cases/adapters/postgresql/postgresql_adapter_test.rb
index 7bf2e7d6..d6165e4d 100644
--- a/test/cases/adapters/postgresql/postgresql_adapter_test.rb
+++ b/test/cases/adapters/postgresql/postgresql_adapter_test.rb
@@ -25,8 +25,10 @@ def teardown
       end
 
       def test_database_exists_returns_false_when_the_database_does_not_exist
-        [ { database: "non_extant_database", adapter: "postgresql" },
-          { database: "non_extant_database", adapter: "cockroachdb" } ].each do |config|
+        config_base = ActiveRecord::Base.configurations.configs_for(env_name: "arunit", name: "primary").configuration_hash
+        [ config_base.merge(database: "non_extant_database", adapter: "cockroachdb"),
+          config_base.merge(database: "non_extant_database", adapter: "postgresql")
+          ].each do |config|
           assert_not ActiveRecord::ConnectionAdapters::CockroachDBAdapter.database_exists?(config),
                     "expected database #{config[:database]} to not exist"
         end
diff --git a/test/cases/helper_cockroachdb.rb b/test/cases/helper_cockroachdb.rb
index 654c8520..b33f13e9 100644
--- a/test/cases/helper_cockroachdb.rb
+++ b/test/cases/helper_cockroachdb.rb
@@ -79,7 +79,7 @@ module TestTimeoutHelper
   def time_it
     t0 = Minitest.clock_time
 
-    timeout_mins = 5
+    timeout_mins = ENV.fetch("TEST_TIMEOUT", 5).to_i
     Timeout.timeout(timeout_mins * 60, Timeout::Error, "Test took over #{timeout_mins} minutes to finish") do
       yield
     end