[routing-manager] new APIs to get state and new CLI commands (#8784)

This commit adds new public OT APIs in `border_routing.h` to get the
current state of `RoutingManager` and to get the current favored
on-link prefix.

This commit also updates CLI `br` commands:
- It moves the CLI `br` implementation into own `cli_br` module.
- It adds `br state` to get the current state
- It changes `br omrprefix`, `br onlinkprefix`, and `br nat64prefix`
  to output both local and favored prefixes when no additional arg
  is provided and allow the use of `local` or `favored` extra arg to
  specify the type.
- It updates the documentation of `br` related commands in the source
  code and also adding `cli/README_BR.md`.

tests/scripts/thread-cert/node.py

@@ -2110,7 +2110,7 @@ class NodeImpl:
         self._expect_done()
 
     def get_br_omr_prefix(self):
-        cmd = 'br omrprefix'
+        cmd = 'br omrprefix local'
         self.send_command(cmd)
         return self._expect_command_output()[0]
 
@@ -2124,7 +2124,7 @@ class NodeImpl:
         return omr_prefixes
 
     def get_br_on_link_prefix(self):
-        cmd = 'br onlinkprefix'
+        cmd = 'br onlinkprefix local'
         self.send_command(cmd)
         return self._expect_command_output()[0]
 
@@ -2137,12 +2137,12 @@ class NodeImpl:
         return prefixes
 
     def get_br_nat64_prefix(self):
-        cmd = 'br nat64prefix'
+        cmd = 'br nat64prefix local'
         self.send_command(cmd)
         return self._expect_command_output()[0]
 
     def get_br_favored_nat64_prefix(self):
-        cmd = 'br favorednat64prefix'
+        cmd = 'br nat64prefix favored'
         self.send_command(cmd)
         return self._expect_command_output()[0].split(' ')[0]