Hi fotonut,
Haven't done much with Pivot Tables yet, so these are more observations than a solution.
Your Pivot Table here seems to be doing what you've told it to do, but not what you intended to tell it to do.
The first column tells it to group and sort the rows by date, using Year as the group size,
For the second column, you placed the Rainfall data token in the Values box, telling Numbers you wanted to do some calculations with that data. You accepted the default calculation of SUM, and the table correctly displays the total rainfall for each year on the row for that year, and the Grand Total for all years recorded in the Footer row of that column.
In the third column, you placed the token for this column in the Values box as you did with Rainfall. According to the information on the token, you want the sum of the data in this column for each year (and the grand total of all the values in this column in the footer row.
Note that, except for the partial year listed in the main table for the last year, all of these annual totals are one of the other of two values: 2384 or 2382. The two larger numbers appear in the rows for 2016 and 2020—both leap years, with one more row (day) in February than the others.
The light clicked on… The table is doing what it was told: SUM the numbers in the Month column, where the numbers are the month number of each day the rain was recorded.
What to do:
Click on the circle to the right of (Year) to open a menu.

And change it to the setting shown in the image above.
No time to go into further details, so do some experimenting. I'll try to return later to decribe and show what I did with the same data table setup as yours (but random data).
Regards,
Barry