R Under development (unstable) (2023-08-09 r84924 ucrt) -- "Unsuffered Consequences"
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> suppressPackageStartupMessages(library(stars))
> # predict:
> tif = system.file("tif/L7_ETMs.tif", package = "stars")
> (x = read_stars(tif))
stars object with 3 dimensions and 1 attribute
attribute(s):
             Min. 1st Qu. Median     Mean 3rd Qu. Max.
L7_ETMs.tif     1      54     69 68.91242      86  255
dimension(s):
     from  to  offset delta                     refsys point x/y
x       1 349  288776  28.5 SIRGAS 2000 / UTM zone 25S FALSE [x]
y       1 352 9120761 -28.5 SIRGAS 2000 / UTM zone 25S FALSE [y]
band    1   6      NA    NA                         NA    NA    
> st_crs(x) = st_crs(x) # cleans trailing space
> model = lm(x~L7_ETMs.tif, head(as.data.frame(x), 50))
> x = predict(x, model)
> 
> (y = read_stars(tif, proxy = TRUE))
stars_proxy object with 1 attribute in 1 file(s):
$L7_ETMs.tif
[1] "[...]/L7_ETMs.tif"

dimension(s):
     from  to  offset delta                     refsys point x/y
x       1 349  288776  28.5 SIRGAS 2000 / UTM zone 25S FALSE [x]
y       1 352 9120761 -28.5 SIRGAS 2000 / UTM zone 25S FALSE [y]
band    1   6      NA    NA                         NA    NA    
> (yp = predict(y, model))
stars_proxy object with 1 attribute in 1 file(s):
$L7_ETMs.tif
[1] "[...]/L7_ETMs.tif"

dimension(s):
     from  to  offset delta                     refsys point x/y
x       1 349  288776  28.5 SIRGAS 2000 / UTM zone 25S FALSE [x]
y       1 352 9120761 -28.5 SIRGAS 2000 / UTM zone 25S FALSE [y]
band    1   6      NA    NA                         NA    NA    
call_list:
[[1]]
predict(object = object, model = model)
attr(,".Environment")
<environment: 0x0000029acb35c0e8>

This object has pending lazy operations: dimensions as printed may not reflect this.
> all.equal(x, st_as_stars(yp))
[1] TRUE
> 
> yy = st_set_dimensions(y, 3, values = paste0("band", 1:6))
> (y_spl = split(yy, 3))
stars_proxy object with 1 attribute in 1 file(s):
$L7_ETMs.tif
[1] "[...]/L7_ETMs.tif"

dimension(s):
     from  to  offset delta                     refsys point          values
x       1 349  288776  28.5 SIRGAS 2000 / UTM zone 25S FALSE            NULL
y       1 352 9120761 -28.5 SIRGAS 2000 / UTM zone 25S FALSE            NULL
band    1   6      NA    NA                         NA    NA band1,...,band6
     x/y
x    [x]
y    [y]
band    
call_list:
[[1]]
split(x = x, 3)
attr(,".Environment")
<environment: 0x0000029acbc5eb30>

This object has pending lazy operations: dimensions as printed may not reflect this.
> as.data.frame(st_as_stars(split(yy, 3)))[1:3,]
         x       y band1 band2 band3 band4 band5 band6
1 288790.5 9120747    69    56    46    79    86    46
2 288819.0 9120747    69    57    49    75    88    49
3 288847.5 9120747    63    52    45    66    75    41
> 
> proc.time()
   user  system elapsed 
   2.18    0.34    2.51