Improve Coroutines transaction API

As a follow-up of gh-22915, the purpose of this commit is to improve
Coroutines programmatic transaction API to make it more consistent with
the Java one and more idiomatic.

For suspending functions, this commit changes the
TransactionalOperator.transactional extension with a suspending lambda
parameter to a TransactionalOperator.executeAndAwait one which is
conceptually closer to TransactionalOperator.execute Java API so more
consistent.

For Flow, the TransactionalOperator.transactional extension is correct
but would be more idiomatic as a Flow extension.

This commit also adds code samples to the reference documentation.

Closes gh-23627

src/docs/asciidoc/languages/kotlin.adoc

@@ -577,8 +577,51 @@ class UserHandler(builder: WebClient.Builder) {
 === Transactions
 
 Transactions on Coroutines are supported via the programmatic variant of the Reactive
-transaction management provided as of Spring Framework 5.2. `TransactionalOperator.transactional`
-extensions with suspending lambda and Kotlin `Flow` parameter are provided for that purpose.
+transaction management provided as of Spring Framework 5.2.
+
+For suspending functions, a `TransactionalOperator.executeAndAwait` extension is provided.
+
+[source,kotlin,indent=0]
+----
+    import org.springframework.transaction.reactive.executeAndAwait
+
+    class PersonRepository(private val operator: TransactionalOperator) {
+
+        suspend fun initDatabase() = operator.executeAndAwait {
+            insertPerson1()
+            insertPerson2()
+        }
+
+        private suspend fun insertPerson1() {
+            // INSERT SQL statement
+        }
+
+        private suspend fun insertPerson2() {
+            // INSERT SQL statement
+        }
+    }
+----
+
+For Kotlin `Flow`, a  `Flow<T>.transactional` extension is provided.
+
+[source,kotlin,indent=0]
+----
+    import org.springframework.transaction.reactive.transactional
+
+    class PersonRepository(private val operator: TransactionalOperator) {
+
+        fun updatePeople() = findPeople().map(::updatePerson).transactional(operator)
+
+        private fun findPeople(): Flow<Person> {
+            // SELECT SQL statement
+        }
+
+        private suspend fun updatePerson(person: Person): Person {
+            // UPDATE SQL statement
+        }
+    }
+----
+
 
 [[kotlin-spring-projects-in-kotlin]]
 == Spring Projects in Kotlin