BUG: Fix DataFrame.at/iat raising ValueError when storing list-like in a single cell

[tinezivic]

• closes BUG: setting item to iterable with .at fails when column doesn't exist or has wrong dtype #61223
• Tests added and passed
• All code checks passed
• Added type annotations to new arguments/methods/functions.
• Added an entry in the latest doc/source/whatsnew/v3.1.0.rst file
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Problem

DataFrame.at and DataFrame.iat raise ValueError when storing a list-like
value (list, tuple, np.ndarray, etc.) into a single cell of a column that
either does not yet exist or has a non-object dtype.

>>> df = pd.DataFrame({"A": [1, 2, 3]})
>>> df.at["a", "B"] = [10, 20, 30]  # new column → ValueError
>>> df.at["b", "A"] = [100, 200]    # int64 column → ValueError
>>> df.iat[0, 0] = [99, 88, 77]     # iat → ValueError

Root cause

_set_value in frame.py falls into the except branch and calls
.loc[index, col] = value. pandas .loc interprets a list-like value as a
multi-row assignment (set multiple rows), not a single-cell assignment, which
raises ValueError: Must have equal len keys and value.

Columns with object dtype already work because column_setitem in the try
block succeeds — they never reach the broken .loc fallback.

Fix

Intercept list-like values (excluding dict, which has special .loc
semantics, and slice, which is used for row-level assignment) before the
try/except block. Ensure the column has object dtype first — casting if it
exists with a non-object dtype, or creating a new object-dtype column if it
does not — then call _mgr.column_setitem directly.

AI Disclosure

I used GitHub Copilot (Claude Sonnet 4.6) to develop this pull request end-to-end:
root cause analysis, fix implementation, tests, and whatsnew entry. I prompted it
to follow AGENTS.md. I reviewed all generated code and understand the changes made.

[jbrockmendel]

i think this is unrelated, seems to have snuck in to several of your PRs?

[tinezivic]

Done, thanks for catching this. I’ve reverted the unrelated changes that slipped in from #62518 / #65118, including:

• the cols_droplevel check (restored to not .any())
• the allow_duplicates signature/type changes in insert()
• the allow_duplicates signature/type changes in reset_index()
• the related allow_duplicates guard logic

This PR now contains only the #61223 at/iat list-like single-cell fix. Revert commit: 36e9f68.