I want to model the movement of fish. Therefore I get a bathymetric map from gebco and masked the land masses.

library(terra)
tif_file <- "~/path_to/GEBCO_map.tif"
map <- rast(tif_file)
map <- ifel(map >= 0, NA, abs(map))

until here I have everything under control. Now I want to change the resolution of the map to a coarser scale and I need to change the coordinates reference.

print(res(map))
[1] 0.004166667 0.004166667 
# I want to change that to 100x100

coord. ref. : lon/lat WGS 84 (EPSG:4326) 
# I want to change that to coord. ref. : WGS 84 / UTM zone 29N (EPSG:32629) 
# for that I have a reference map (mapE) 
map_reprojected <- project(map, crs(mapE))

# Trying to get the desired resolution (e.g., 100 x 100 meters)

new_resolution <- c(100, 100)
current_resolution <- res(map)

# Calculate the target number of rows and columns based on the desired resolution

target_ncols <- ncol(map) * (current_resolution[1] / new_resolution[1])
target_nrows <- nrow(map) * (current_resolution[2] / new_resolution[2])

# Create a dummy raster with the new resolution but same number of rows and columns

dummy_raster <- rast(ext(map), nrows = round(target_nrows), ncols = round(target_ncols), resolution = new_resolution)

# Resample the original map to the new resolution while keeping the number of rows and columns

map_resampled <- resample(map_reprojected, res = new_resolution, method = "bilinear")

My problem is, that once I adjust the resolution, my dimensions of the map go to 1,1,1 and I have NAs everywhere. Is there any way to change just the resolution of the map?
Changing the coord.reference works but is the map still correct then ? When I plot it, it looks worbed.