+doc #20521 Enrich docs and tests regarding empty strings used in matchers (#20719)

akka-docs/rst/java/http/routing-dsl/directives/path-directives/path.rst

@@ -24,6 +24,10 @@ a ``path`` directive will always be empty).
 Depending on the type of its ``PathMatcher`` argument the ``path`` directive extracts zero or more values from the URI.
 If the match fails the request is rejected with an :ref:`empty rejection set <empty rejections>`.
 
+.. note:: The empty string (also called empty word or identity) is a **neutral element** of string concatenation operation,
+ so it will match everything, but remember that ``path`` requires whole remaining path being matched, so (``/``) will succeed
+ and (``/whatever``) will fail. The :ref:`-pathPrefix-java-` provides more liberal behaviour.
+
 
 Example
 -------

akka-docs/rst/java/http/routing-dsl/directives/path-directives/pathPrefix.rst

@@ -18,6 +18,9 @@ As opposed to its :ref:`-rawPathPrefix-java-` counterpart ``pathPrefix`` automat
 Depending on the type of its ``PathMatcher`` argument the ``pathPrefix`` directive extracts zero or more values from
 the URI. If the match fails the request is rejected with an :ref:`empty rejection set <empty rejections>`.
 
+.. note:: The empty string (also called empty word or identity) is a **neutral element** of string concatenation operation,
+ so it will match everything and consume nothing. The :ref:`-path-java-` provides more strict behaviour.
+
 
 Example
 -------

akka-docs/rst/scala/http/routing-dsl/directives/path-directives/path.rst

@@ -31,6 +31,10 @@ a ``path`` directive will always be empty).
 Depending on the type of its ``PathMatcher`` argument the ``path`` directive extracts zero or more values from the URI.
 If the match fails the request is rejected with an :ref:`empty rejection set <empty rejections>`.
 
+.. note:: The empty string (also called empty word or identity) is a **neutral element** of string concatenation operation,
+ so it will match everything, but remember that ``path`` requires whole remaining path being matched, so (``/``) will succeed
+ and (``/whatever``) will fail. The :ref:`-pathPrefix-` provides more liberal behaviour.
+
 
 Example
 -------

akka-docs/rst/scala/http/routing-dsl/directives/path-directives/pathPrefix.rst

@@ -25,6 +25,9 @@ As opposed to its :ref:`-rawPathPrefix-` counterpart ``pathPrefix`` automaticall
 Depending on the type of its ``PathMatcher`` argument the ``pathPrefix`` directive extracts zero or more values from
 the URI. If the match fails the request is rejected with an :ref:`empty rejection set <empty rejections>`.
 
+.. note:: The empty string (also called empty word or identity) is a **neutral element** of string concatenation operation,
+ so it will match everything and consume nothing. The :ref:`-path-` provides more strict behaviour.
+
 
 Example
 -------