How to calculate the partial R squared for a linear model with factor interaction in R

Question

I have a linear model where my response Y is say the percentage (proportion) of fat in milk. I have two explanatory variables one (x1) is a continuous variable, the other (z) is a three level factor.

I now do the regression in R as:

contrasts(z) <- "contr.sum"
model<-lm(logit(Y) ~ log(x1)*z)

the model summary gives me the R2 of this model . However, I want to find out the importance of x1 in my model. I can look at the p-value if the slope is statistically different from 0, but this does not tell me if x1 is actually a good predictor.

Is there a way to get the partial R2 for this model and the overall effect of x1? As this model includes an interaction I am not sure how to calculate this and if there is one unique solution or if I get a partial R2 for the main effect of x1 and a partial R2 for main effect of x1 plus its interaction.

Or would it be better to avoid partial R2 and explain the magnitude of the slope of the main effect and interaction. But given my logit transformation I am not sure if this has any practical meaning for say how log(x1) changes the log odds ratio of % fat in milk.

Thanks.

-I tried to fit the model without the interaction and without the factor to get a usual R2 , but this would not be my preferred solution and I would like to get the partial R2 when specifying a full model.

Update: As requested in a comment, here the output from the summary(model). As written above z is sum contrast coded.

Call:
lm(formula = y ~ log(x1) * z, data = mydata)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.21240 -0.09487  0.03282  0.13588  0.85941 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -2.330678   0.034043 -68.462  < 2e-16 ***
log(x1)     -0.012948   0.005744  -2.254  0.02454 *  
z1           0.140710   0.048096   2.926  0.00357 ** 
z2          -0.348526   0.055156  -6.319 5.17e-10 ***
log(x1):z1   0.017051   0.008095   2.106  0.03558 *  
log(x1):z2  -0.028201   0.009563  -2.949  0.00331 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2288 on 594 degrees of freedom
Multiple R-squared:  0.1388,    Adjusted R-squared:  0.1315 
F-statistic: 19.15 on 5 and 594 DF,  p-value: < 2.2e-16

Update: As requested in a comment, here the output from

print(aov(model))

Call:
   aov(formula = model)

Terms:
                  log(x1)         z log(x1):z Residuals
Sum of Squares   0.725230  3.831223  0.456677 31.105088
Deg. of Freedom         1         2         2       594

Residual standard error: 0.228835
Estimated effects may be unbalanced.
As written above, z is sum contrast coded.