Why is coord_sf needed to plot a geom_raster with ggplot2?

Question

Why is coord_sf() needed to plot a geom_raster in ggplot2 and what exactly does coord_sf() do?

According to ggplot2's Map project's documentation: coord_map projects a portion of spherical earth onto a flat, 2D plane. But why do we need this if we have transformed our data into a projected coordinate system? My second plot below uses a projected raster, but it is still stretched.

Is coord_sf() needed because geom_raster is not necessarily spatial and therefore ggplot2 would not automatically infer a projection from it as it would with geom_sf? For example, ggplot's Visualise sf objects documentation, states that geom_sf() adds coord_sf() for you (and it is therefore unnecessary to add it --i.e. it is expecting geom_sf() to spatial).

gglot2 states: crs: The CRS into which all data should be projected before plotting. If not specified, will use the CRS defined in the first sf layer in the plot. But geom_raster is a non-sf geom. So in this case, is coord_sf() when used with geom_raster() as in plot 3 below re-projecting my raster into Mercator? This would not be my assumption as it is displayed in meters. Further confounding is that when I force the ggplot2 map in plot 4 to be in EPSG 23032, the map is in degrees instead of expected meters.

  library(terra)
  library(ggplot2)

  # Sample raster data from terra package
  path_lux <- system.file("ex/elev.tif", package="terra")
  f <- system.file("ex/elev.tif", package="terra")
  
  # Create raster object, projected raster object, dataframes from each
  luxembourg_elev <- terra::rast(f)
  df_lux <- as.data.frame(luxembourg_elev, xy = TRUE)
  luxembourg_elev_23032 <- terra::project(luxembourg_elev, y ="epsg:23032")
  df_lux_23032 <- as.data.frame(luxembourg_elev_23032, xy = TRUE)
  
  # Plot 1: geographic crs looks stretched
  plot_lux <- ggplot() +
    geom_raster(data= df_lux, aes(x = x, y = y, fill = elevation))

  # Plot 2: projected crs still looks stretched
  plot_lux_23032 <- ggplot() +
    geom_raster(data= df_lux_23032, aes(x = x, y = y, fill = elevation))
  
  # Plot 3: coord_sf() produces un-stretched plot
  plot_lux_23032_coord <- ggplot() +
    geom_raster(data= df_lux_23032, aes(x = x, y = y, fill = elevation)) + coord_sf()
  
  # Plot 4: I try to specify EPSG 23032 (also no longer looks stretched but is confusingly in degrees

  plot_lux_23032_2 <- ggplot() +
  geom_raster(data= df_lux_23032, aes(x = x, y = y, fill = elevation)) + coord_sf(default_crs = sf::st_crs(23032))