Polars milliseconds since midnight into datetime

Question

I have a Polars data frame in the following format:

shape: (500_259, 2)
┌───────────┬──────────┐
│ ms_of_day ┆ date     │
│ ---       ┆ ---      │
│ i64       ┆ i64      │
╞═══════════╪══════════╡
│ 0         ┆ 20240729 │
│ 300000    ┆ 20240729 │
│ 600000    ┆ 20240729 │
│ 900000    ┆ 20240729 │
│ 1200000   ┆ 20240729 │
│ …         ┆ …        │
│ 85200000  ┆ 20240729 │
│ 85500000  ┆ 20240729 │
│ 85800000  ┆ 20240729 │
│ 86100000  ┆ 20240729 │
│ 86400000  ┆ 20240729 │
└───────────┴──────────┘

ms_of_day represents the milliseconds since midnight so 30000 = 12:05 AM, 60000 = 12:10 AM, etc. The date column is obviously in '%Y%m%d' format. The date column is straight forward enough to convert to a datetime column with...

.with_columns(
            new_date = pl.col('date').cast(pl.String).str.to_datetime('%Y%m%d'))

shape: (500_259, 3)
┌───────────┬──────────┬─────────────────────┐
│ ms_of_day ┆ date     ┆ new_date            │
│ ---       ┆ ---      ┆ ---                 │
│ i64       ┆ i64      ┆ datetime[μs]        │
╞═══════════╪══════════╪═════════════════════╡
│ 0         ┆ 20240729 ┆ 2024-07-29 00:00:00 │
│ 300000    ┆ 20240729 ┆ 2024-07-29 00:00:00 │
│ 600000    ┆ 20240729 ┆ 2024-07-29 00:00:00 │
│ 900000    ┆ 20240729 ┆ 2024-07-29 00:00:00 │
│ 1200000   ┆ 20240729 ┆ 2024-07-29 00:00:00 │
│ …         ┆ …        ┆ …                   │
│ 85200000  ┆ 20240729 ┆ 2024-07-29 00:00:00 │
│ 85500000  ┆ 20240729 ┆ 2024-07-29 00:00:00 │
│ 85800000  ┆ 20240729 ┆ 2024-07-29 00:00:00 │
│ 86100000  ┆ 20240729 ┆ 2024-07-29 00:00:00 │
│ 86400000  ┆ 20240729 ┆ 2024-07-29 00:00:00 │
└───────────┴──────────┴─────────────────────┘

but I'm struggling with how to incorporate ms_of_day column into the new_date column so that the time is also represented correctly. For example, the second row should be 2024-07-29 00:05:00, third row 2024-07-29 00:10:00, etc.