Supplementing age class determination with observation data in R

Question

I am working with a dataset of yearly observations structured like this

data<-data.frame(ID=c(rep("A",6),rep("B",12),rep("C",9)),
             FeatherID=rep(c("a","b","c"),9),
             Year=c(rep(2020,3),rep(2021,3),rep(2017,3),rep(2019,3),rep(2020,3),rep(2021,3),rep(2018,3),rep(2019,3),rep(2020,3)),
             Age_Field=c(rep("1CY",3),rep("2CY",3),rep("1CY",3),rep(">2CY",3),rep(">2CY",3),rep(">2CY",3),rep(">2CY",3),rep(">2CY",3),rep(">2CY",3)))

   ID FeatherID Year Age_Field
1   A         a 2020       1CY
2   A         b 2020       1CY
3   A         c 2020       1CY
4   A         a 2021       2CY
5   A         b 2021       2CY
6   A         c 2021       2CY
7   B         a 2017       1CY
8   B         b 2017       1CY
9   B         c 2017       1CY
10  B         a 2019      >2CY
11  B         b 2019      >2CY
12  B         c 2019      >2CY
13  B         a 2020      >2CY
14  B         b 2020      >2CY
15  B         c 2020      >2CY
16  B         a 2021      >2CY
17  B         b 2021      >2CY
18  B         c 2021      >2CY
19  C         a 2018      >2CY
20  C         b 2018      >2CY
21  C         c 2018      >2CY
22  C         a 2019      >2CY
23  C         b 2019      >2CY
24  C         c 2019      >2CY
25  C         a 2020      >2CY
26  C         b 2020      >2CY
27  C         c 2020      >2CY

For each yearly observation the age class of the individual is determined as first year (1CY), second year (2CY) or older (>2CY). I would like to combine this age class data with the information given by the year the individuals are observed in, in order to calculate a column with the true (minimum) age of each individual in each year, corresponding to this for the earlier example

 > data.frame(Age_True=c(rep(0,3),rep(1,3),rep(0,3),rep(2,3),rep(3,3),rep(4,3),rep(2,3),rep(3,3),rep(4,3)))
   Age_True
1         0
2         0
3         0
4         1
5         1
6         1
7         0
8         0
9         0
10        2
11        2
12        2
13        3
14        3
15        3
16        4
17        4
18        4
19        2
20        2
21        2
22        3
23        3
24        3
25        4
26        4
27        4

I've been trying different ways to do this, but I can't quite figure it out. Hopefully someone knows a way to do this. Cheers!