How to reindex a datetime-based multiindex in pandas

I have a dataframe that counts the number of times an event has occured per user per day. Users may have 0 events per day and (since the table is an aggregate from a raw event log) rows with 0 events are missing from the dataframe. I would like to add these missing rows and group the data by week so that each user has one entry per week (including 0 if applicable).

Here is an example of my input:

import numpy as np
import pandas as pd

np.random.seed(42)

df = pd.DataFrame({
    "person_id": np.arange(3).repeat(5),
    "date": pd.date_range("2022-01-01", "2022-01-15", freq="d"),
    "event_count": np.random.randint(1, 7, 15),
})

# end of each week
# Note: week 2022-01-23 is not in df, but should be part of the result
desired_index = pd.to_datetime(["2022-01-02", "2022-01-09", "2022-01-16", "2022-01-23"])

df

|    |   person_id | date                |   event_count |
|---:|------------:|:--------------------|--------------:|
|  0 |           0 | 2022-01-01 00:00:00 |             4 |
|  1 |           0 | 2022-01-02 00:00:00 |             5 |
|  2 |           0 | 2022-01-03 00:00:00 |             3 |
|  3 |           0 | 2022-01-04 00:00:00 |             5 |
|  4 |           0 | 2022-01-05 00:00:00 |             5 |
|  5 |           1 | 2022-01-06 00:00:00 |             2 |
|  6 |           1 | 2022-01-07 00:00:00 |             3 |
|  7 |           1 | 2022-01-08 00:00:00 |             3 |
|  8 |           1 | 2022-01-09 00:00:00 |             3 |
|  9 |           1 | 2022-01-10 00:00:00 |             5 |
| 10 |           2 | 2022-01-11 00:00:00 |             4 |
| 11 |           2 | 2022-01-12 00:00:00 |             3 |
| 12 |           2 | 2022-01-13 00:00:00 |             6 |
| 13 |           2 | 2022-01-14 00:00:00 |             5 |
| 14 |           2 | 2022-01-15 00:00:00 |             2 |

This is how my desired result looks like:

|    |   person_id | level_1             |   event_count |
|---:|------------:|:--------------------|--------------:|
|  0 |           0 | 2022-01-02 00:00:00 |             9 |
|  1 |           0 | 2022-01-09 00:00:00 |            13 |
|  2 |           0 | 2022-01-16 00:00:00 |             0 |
|  3 |           0 | 2022-01-23 00:00:00 |             0 |
|  4 |           1 | 2022-01-02 00:00:00 |             0 |
|  5 |           1 | 2022-01-09 00:00:00 |            11 |
|  6 |           1 | 2022-01-16 00:00:00 |             5 |
|  7 |           1 | 2022-01-23 00:00:00 |             0 |
|  8 |           2 | 2022-01-02 00:00:00 |             0 |
|  9 |           2 | 2022-01-09 00:00:00 |             0 |
| 10 |           2 | 2022-01-16 00:00:00 |            20 |
| 11 |           2 | 2022-01-23 00:00:00 |             0 |

I can produce it using:

(
    df
    .groupby(["person_id", pd.Grouper(key="date", freq="w")]).sum()
    .groupby("person_id").apply(
        lambda df: (
            df
            .reset_index(drop=True, level=0)
            .reindex(desired_index, fill_value=0))
        )
    .reset_index()
)

However, according to the docs of reindex, I should be able to use it with level=1 as a kwarg directly and without having to do another groupby. However, when I do this I get an "inner join" of the two indices instead of an "outer join":

result = (
    df
    .groupby(["person_id", pd.Grouper(key="date", freq="w")]).sum()
    .reindex(desired_index, level=1)
    .reset_index()
)

|    |   person_id | date                |   event_count |
|---:|------------:|:--------------------|--------------:|
|  0 |           0 | 2022-01-02 00:00:00 |             9 |
|  1 |           0 | 2022-01-09 00:00:00 |            13 |
|  2 |           1 | 2022-01-09 00:00:00 |            11 |
|  3 |           1 | 2022-01-16 00:00:00 |             5 |
|  4 |           2 | 2022-01-16 00:00:00 |            20 |

Why is that, and how am I supposed to use df.reindex correctly?

---

I have found a similar SO question on reindexing a multi-index level, but the accepted answer there uses df.unstack, which doesn’t work for me, because not every level of my desired index occurs in my current index (and vice versa).