Resampling of categorical column in pandas data frame

Update after your edit:

out = df.set_index(pd.to_datetime(df.index).floor('T')) \
        .groupby(level=0)['category'] \
        .apply(lambda x: x.value_counts().idxmax())
print(out)

# Output
2021-06-03 01:19:00    1
2021-06-03 01:20:00    0
2021-06-03 01:21:00    1
2021-06-04 01:19:00    0
2021-06-04 01:22:00    0
2021-06-05 02:20:00    0
Name: category, dtype: int64

Old answer

# I used 'D' instead of 'T'
>>> df.set_index(df.index.floor('D')).groupby(level=0).count()
            category
2021-06-03         6
2021-06-04         2
2021-06-06         1
2021-06-08         1
2021-06-25         1
2021-06-29         6
2021-06-30         3

# OR

>>> df.set_index(df.index.floor('D')).groupby(level=0).sum()
            category
2021-06-03         2
2021-06-04         0
2021-06-06         1
2021-06-08         1
2021-06-25         0
2021-06-29         3
2021-06-30         1