Cohen's f2 test

The formula here makes it look at is could be able to compare any nested models that have an R2. But should it be under test_wald(), or a separate test_f2()? The latter would make sense (as test_wald is quite limited), but then @mattansb said the p-value than for the former, so it's roughly equivalent?

m1 <- lm(mpg ~ ., data=mtcars)
m2 <- lm(mpg ~ cyl + vs, data=mtcars)

effectsize::cohens_f_squared(m1, model2 = m2)
#> Loading required namespace: performance
#> Cohen's f2 (partial) |       90% CI | R2_delta
#> ----------------------------------------------
#> 1.07                 | [0.06, 1.79] |     0.14
performance::test_wald(m1, m2)
#>   Name Model df df_diff        F          p
#> 1   m1    lm 21      NA       NA         NA
#> 2   m2    lm 29      -8 2.820169 0.02710374

^{Created on 2021-02-09 by the reprex package (v0.2.1)}

Start with the linked effectsize Cohen's f documentation and the example calls to effectsize::cohens_f_squared() and performance::test_wald(). Determine whether Cohen's f2 belongs in test_wald() or needs a separate test_f2(), and clarify how its p-value should relate to the existing output. Done means the design decision and expected behavior are documented.