Fix markdown table rendering issue.

The table data elements were not interacting well with inline styles (in the rich sense) and the table data element would have its content overridden every time we found another excerpt of text with a different style.

CHANGELOG.md

@@ -5,6 +5,12 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
+## Unreleased
+
+### Fixed
+
+- Markdown table rendering issue with inline styles and links https://github.com/Textualize/rich/issues/3115
+
 ## [13.5.2] - 2023-08-01
 
 ### Fixed

rich/markdown.py

@@ -314,7 +314,7 @@ class TableDataElement(MarkdownElement):
 
     @classmethod
     def create(cls, markdown: "Markdown", token: Token) -> "MarkdownElement":
-        style = str(token.attrs.get("style" "")) or ""
+        style = str(token.attrs.get("style")) or ""
 
         justify: JustifyMethod
         if "text-align:right" in style:
@@ -330,15 +330,18 @@ def create(cls, markdown: "Markdown", token: Token) -> "MarkdownElement":
         return cls(justify=justify)
 
     def __init__(self, justify: JustifyMethod) -> None:
-        self.content: TextType = ""
+        self.content: Text = Text("", justify=justify)
         self.justify = justify
 
     def on_text(self, context: "MarkdownContext", text: TextType) -> None:
-        plain = text.plain if isinstance(text, Text) else text
-        style = text.style if isinstance(text, Text) else ""
-        self.content = Text(
+        text = Text(text) if isinstance(text, str) else text
+        text.stylize(context.current_style)
+        self.content.append_text(text)
+        # plain = text.plain if isinstance(text, Text) else text
+        # self.content.append(plain, context.style_stack.current)
+        """ self.content += Text(
             plain, justify=self.justify, style=context.style_stack.current
-        )
+        ) """
 
 
 class ListElement(MarkdownElement):