Ignore the date column we just need to merge based on YYYY-MM .
First table has one rwo for each month but second table may have multiple rows for each month. First rows matching month’s data should be merged to all of them.

data-frame 1:

2020-01-01   1.480
2020-02-01   1.620
2020-03-01   1.000
2020-04-01   1.000
2020-05-01   1.950
2020-06-01   1.080
2020-07-01   1.480
2020-08-01   1.620
2020-09-01   1.000
2020-10-01   1.000
2020-11-01   1.950
2020-12-01   1.080
2021-01-01   11.480
2021-02-01   12.620
2021-03-01   13.000
2021-04-01   14.000
2021-05-01   15.950
2021-06-01   16.080
2021-07-01   17.480
2021-08-01   18.620
2021-09-01   19.000
2021-10-01   10.000
2021-11-01   11.950
2021-12-01   12.080
2022-01-01   21.480
2022-02-01   22.620
2022-03-01   23.000
2022-04-01   24.000
2022-05-01   25.950
2022-06-01   26.080
2022-07-01   27.480
2022-08-01   28.620
2022-09-01   29.000
2022-10-01   30.000
2022-11-01   31.950
2022-12-01   32.080
2023-01-01   31.480
2023-02-01   31.620
2023-03-01   32.000
2023-04-01   32.200
2023-05-01   31.950
2023-06-01   32.080
2023-07-01   33.080

data-frame 2:

2020-01-15            NaN             NaN             111               111 
2020-02-25            NaN             333             NaN               204 
2021-02-22            123             NaN             NaN               111 
2023-07-18            NaN             324             111               NaN 
2023-03-15            NaN             NaN             NaN               205  

desired data-frame:

2020-01-15     1.480       NaN             NaN             111               111
2020-02-25     1.620       NaN             333             NaN               204 
2021-02-22     1.620       123             NaN             NaN               111 
2023-07-18     33.080      NaN             324             111               NaN 
2023-03-15     32.000      NaN             NaN             NaN               205