Is it possible to compare an R2 value across three independent samples? I am familiar with the Fisher r to z test, but this is only for correlation coefficients, correct?

For instance, say I have three different age groups, three doses of medication, and then a DV of a test score:

I test a model DV = age + med_dose + age*med_dose and I get a significant interaction between age and med dose.
Then I separate into the three different age groups and graph group means for each med dose and age. I find that the oldest age group seems to follow an inverted-U shape pattern (i.e., the medium dose of medicine has the best effect on performance). I also find that the younger two age groups don't seem to have much difference at all between the different medication doses on performance.
So, I could look at contrasts comparing each medication dose within each age group (e.g., so I could say that p<0.05 for a contrast comparing low dose to medium dose and medium dose to high dose in the oldest age group, but these same two contrasts are not significant in the younger two age groups).

However, my question is: can I compare an R2 value between these three age groups? Could I fit a quadratic model to each age group (DV = med_dose + med_dose^2 for each age group) and then say that the "fit" (R2) is the best for the oldest age group...significantly better than the quadratic fit for the younger two age groups?

Can I do something like Fisher r to z to compare the R2 fits? Is this adding beneficial info. to my analysis rather than just comparing mean scores based on dose within each group?

What if we have unequal sample sizes between the different age groups?