fix: handle multiple handler's envs on same doc.

Instead of a boolean of has any env been updated, track by handle name
which env has been updated.

References: mkdocstrings#201
Fixes: 502

src/mkdocstrings/extension.py

@@ -78,7 +78,7 @@ def __init__(
         self._config = config
         self._handlers = handlers
         self._autorefs = autorefs
-        self._updated_env = False
+        self._updated_envs: list = []
 
     def test(self, parent: Element, block: str) -> bool:
         """Match our autodoc instructions.
@@ -197,10 +197,10 @@ def _process_block(
                 log.error(f"Error reading page '{self._autorefs.current_page}':")
             raise PluginError(f"Could not collect '{identifier}'") from exception
 
-        if not self._updated_env:
+        if handler_name not in self._updated_envs:  # We haven't seen this handler before on this document.
             log.debug("Updating renderer's env")
             handler._update_env(self.md, self._config)  # noqa: WPS437 (protected member OK)
-            self._updated_env = True
+            self._updated_envs.append(handler_name)
 
         log.debug("Rendering templates")
         try:

src/mkdocstrings/handlers/base.py

@@ -298,6 +298,7 @@ def update_env(self, md: Markdown, config: dict) -> None:  # noqa: W0613 (unused
         self.env.filters["heading"] = self.do_heading
 
     def _update_env(self, md: Markdown, config: dict):
+        """Update our handler to point to our configured Markdown instance, grabbing some of the config from `md`."""
         extensions = config["mdx"] + [MkdocstringsInnerExtension(self._headings)]
 
         new_md = Markdown(extensions=extensions, extension_configs=config["mdx_configs"])