See the cats and levels methods. They are used to have rasters that behave like "factors". The issues you describe have been fixed in terra 1.1-17 (on its way to CRAN). For now, what you can do is something along these lines:
library(raster)
f <- "nlcd_agg.grd"
r <- raster(f)
library(terra)
x <- rast(r)
# get the attributes
lev <- levels(r)[[1]]
lev <- lev[, c("ID", "Land.Cover.Class")]
lev[,2] <- as.character(lev[,2])
x <- rast(r)
levels(x) <- lev
is.factor(x)
#[1] TRUE
x
#class : SpatRaster
#dimensions : 101, 121, 1 (nrow, ncol, nlyr)
#resolution : 3750, 3750 (x, y)
#extent : 1394535, 1848285, 1722765, 2101515 (xmin, xmax, ymin, ymax)
#coord. ref. : +proj=aea +lat_0=23 +lon_0=-96 +lat_1=29.5 +lat_2=45.5 +x_0=0 +y_0=0 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
#source : memory
#name : nlcd_2011_landcover_2011_edition_2014_03_31
#min value : Unclassified
#max value :
# legend shows class names
plot(x)
Labels are returned as cell values
x[c(7357, 5047, 7360, 9307)]
# nlcd_2011_landcover_2011_edition_2014_03_31
#1 Perennial Snow/Ice
#2 Open Water
#3 Perennial Snow/Ice
#4 Unclassified
And the categories are stored if you save the raster to a GeoTIFF
z <- writeRaster(x, "test.tif", overwrite=TRUE)
z
ch