Backport PR #41844: DOC: Add .to_xyz to io docs (#42060)

Co-authored-by: Griffin Ansel <[email protected]>

Author: meeseeksmachine

doc/source/reference/io.rst

@@ -13,6 +13,7 @@ Pickling
    :toctree: api/
 
    read_pickle
+   DataFrame.to_pickle
 
 Flat file
 ~~~~~~~~~
@@ -21,6 +22,7 @@ Flat file
 
    read_table
    read_csv
+   DataFrame.to_csv
    read_fwf
 
 Clipboard
@@ -29,30 +31,41 @@ Clipboard
    :toctree: api/
 
    read_clipboard
+   DataFrame.to_clipboard
 
 Excel
 ~~~~~
 .. autosummary::
    :toctree: api/
 
    read_excel
+   DataFrame.to_excel
    ExcelFile.parse
 
+.. currentmodule:: pandas.io.formats.style
+
+.. autosummary::
+   :toctree: api/
+
+   Styler.to_excel
+
+.. currentmodule:: pandas
+
 .. autosummary::
    :toctree: api/
    :template: autosummary/class_without_autosummary.rst
 
    ExcelWriter
 
+.. currentmodule:: pandas.io.json
+
 JSON
 ~~~~
 .. autosummary::
    :toctree: api/
 
    read_json
-   json_normalize
-
-.. currentmodule:: pandas.io.json
+   to_json
 
 .. autosummary::
    :toctree: api/
@@ -67,13 +80,40 @@ HTML
    :toctree: api/
 
    read_html
+   DataFrame.to_html
+
+.. currentmodule:: pandas.io.formats.style
+
+.. autosummary::
+   :toctree: api/
+
+   Styler.to_html
+
+.. currentmodule:: pandas
 
 XML
 ~~~~
 .. autosummary::
    :toctree: api/
 
    read_xml
+   DataFrame.to_xml
+
+Latex
+~~~~~
+.. autosummary::
+   :toctree: api/
+
+   DataFrame.to_latex
+
+.. currentmodule:: pandas.io.formats.style
+
+.. autosummary::
+   :toctree: api/
+
+   Styler.to_latex
+
+.. currentmodule:: pandas
 
 HDFStore: PyTables (HDF5)
 ~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -101,13 +141,15 @@ Feather
    :toctree: api/
 
    read_feather
+   DataFrame.to_feather
 
 Parquet
 ~~~~~~~
 .. autosummary::
    :toctree: api/
 
    read_parquet
+   DataFrame.to_parquet
 
 ORC
 ~~~
@@ -138,6 +180,7 @@ SQL
    read_sql_table
    read_sql_query
    read_sql
+   DataFrame.to_sql
 
 Google BigQuery
 ~~~~~~~~~~~~~~~
@@ -152,6 +195,7 @@ STATA
    :toctree: api/
 
    read_stata
+   DataFrame.to_stata
 
 .. currentmodule:: pandas.io.stata