Avoid unnecessary re-opening of HDF5 files (Closes: pandas-dev#58248) (…

…pandas-dev#58275)

* Avoid unnecessary re-opening of HDF5 files

* Update the whatsnew file

* Move the changelog entry for pandas-dev#58248 to the correct section

doc/source/whatsnew/v3.0.0.rst

@@ -331,6 +331,7 @@ Performance improvements
 - Performance improvement in :meth:`RangeIndex.reindex` returning a :class:`RangeIndex` instead of a :class:`Index` when possible. (:issue:`57647`, :issue:`57752`)
 - Performance improvement in :meth:`RangeIndex.take` returning a :class:`RangeIndex` instead of a :class:`Index` when possible. (:issue:`57445`, :issue:`57752`)
 - Performance improvement in :func:`merge` if hash-join can be used (:issue:`57970`)
+- Performance improvement in :meth:`to_hdf` avoid unnecessary reopenings of the HDF5 file to speedup data addition to files with a very large number of groups . (:issue:`58248`)
 - Performance improvement in ``DataFrameGroupBy.__len__`` and ``SeriesGroupBy.__len__`` (:issue:`57595`)
 - Performance improvement in indexing operations for string dtypes (:issue:`56997`)
 - Performance improvement in unary methods on a :class:`RangeIndex` returning a :class:`RangeIndex` instead of a :class:`Index` when possible. (:issue:`57825`)
@@ -406,7 +407,6 @@ I/O
 - Bug in :meth:`DataFrame.to_string` that raised ``StopIteration`` with nested DataFrames. (:issue:`16098`)
 - Bug in :meth:`read_csv` raising ``TypeError`` when ``index_col`` is specified and ``na_values`` is a dict containing the key ``None``. (:issue:`57547`)
 
-
 Period
 ^^^^^^
 -

pandas/io/pytables.py

@@ -292,14 +292,14 @@ def to_hdf(
             dropna=dropna,
         )
 
-    path_or_buf = stringify_path(path_or_buf)
-    if isinstance(path_or_buf, str):
+    if isinstance(path_or_buf, HDFStore):
+        f(path_or_buf)
+    else:
+        path_or_buf = stringify_path(path_or_buf)
         with HDFStore(
             path_or_buf, mode=mode, complevel=complevel, complib=complib
         ) as store:
             f(store)
-    else:
-        f(path_or_buf)
 
 
 def read_hdf(