Clarification regarding:

This was previously handled more gracefully, but starting from commit 5ff2027 (included in Pillow 11.1.0), all NaN IFDRational values are considered as TiffTags.RATIONAL.

This change in behavior is due to how float('nan') operates in Python:

>>> float('nan') == float('nan')
False
>>> float('nan') > 0
False
>>> float('nan') < 0
False
>>> float('nan') == 0
False

Before commit 5ff2027, the logic used all(v >= 0 for v in values) to determine the tag type. Since any comparison involving float('nan') returns False, the presence of a NaN caused the expression to evaluate to False, resulting in the tag being set to TiffTags.SIGNED_RATIONAL:

                    self.tagtype[tag] = (
                        TiffTags.RATIONAL
                        if all(v >= 0 for v in values)
                        else TiffTags.SIGNED_RATIONAL
                    )

After the commit, the logic was changed to inspect values individually:

                    for v in values:
                        assert isinstance(v, IFDRational)
                        if v < 0:
                            self.tagtype[tag] = TiffTags.SIGNED_RATIONAL
                            break
                        else:
                            self.tagtype[tag] = TiffTags.RATIONAL

This change means that when a value is float('nan'), it does not satisfy the v < 0 condition (nor would it satisfy any other typical comparison), so the tag is now set to TiffTags.RATIONAL by default