`r2_nakagawa()` is **NOT** location invariant when COV is not modelled (and is wrong?)

This is some weird stuff.

library(lme4)
#> Loading required package: Matrix
library(performance)

r2_nakagawa2 <- function(model) {
  y <- insight::get_response(model)
  c(
    Cond. = cor(predict(model, re.form = NULL), y)^2,
    Marg. = cor(predict(model, re.form = NA), y)^2
  )
}


# With COV =================================
m1 <- lmer(Reaction ~ Days + (Days|Subject),
          data = sleepstudy)


# Change location -------
sleepstudy$Days0 <- sleepstudy$Days - 10
m2 <- lmer(Reaction ~ Days0 + (Days0|Subject),
          data = sleepstudy)
#> Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
#> Model failed to converge with max|grad| = 0.00422952 (tol = 0.002, component 1)

r2_nakagawa(m1)
#> # R2 for Mixed Models
#> 
#>   Conditional R2: 0.799
#>      Marginal R2: 0.279
r2_nakagawa(m2) # same
#> # R2 for Mixed Models
#> 
#>   Conditional R2: 0.799
#>      Marginal R2: 0.279

# Validate:
r2_nakagawa2(m1)
#>     Cond.     Marg. 
#> 0.8271703 0.2864714
r2_nakagawa2(m2)
#>     Cond.     Marg. 
#> 0.8271702 0.2864714


# Without COV =================================
m1b <- lmer(Reaction ~ Days + (Days||Subject),
           data = sleepstudy)


# Change location -------
m2b <- lmer(Reaction ~ Days0 + (Days0||Subject),
           data = sleepstudy)


r2_nakagawa(m1b) # different
#> # R2 for Mixed Models
#> 
#>   Conditional R2: 0.702
#>      Marginal R2: 0.415
r2_nakagawa(m2b) # even more different
#> # R2 for Mixed Models
#> 
#>   Conditional R2: 0.864
#>      Marginal R2: 0.183

r2_nakagawa2(m1b) # same as with cov
#>     Cond.     Marg. 
#> 0.8279419 0.2864714
r2_nakagawa2(m2b) # same as with cov
#>     Cond.     Marg. 
#> 0.8244819 0.2864714

^{Created on 2022-06-03 by the reprex package (v2.0.1)}

Start with the r2_nakagawa() entry point and reproduce the lme4 sleepstudy examples in the issue, comparing models with and without covariance and shifted Days values. Determine the intended location-invariant result for models where COV is not modelled; done means the behavior is corrected and covered by an appropriate regression check.