Basically, what you see is what you get. If sf::st_coordinates() returns a column M and/or Z, your feature object has a M and/or Z dimension in addition to the regular X/Y dimensions.

?st_coordinates():

Matrix with coordinates (X, Y, possibly Z and/or M) in rows, possibly followed by integer indicators L1,…,L3 that point out to which structure the coordinate belongs […]

library(sf)
#> Linking to GEOS 3.11.2, GDAL 3.8.2, PROJ 9.3.1; sf_use_s2() is TRUE

# starting with some simple wkt representation of a multilinestring
wkt <- "MULTILINESTRING((0 0, 0 1), (1 1, 1 2, 1 3))"

# some workaround to add M dimension to your multilinestring
x1 <- wkt |>  
  st_as_sfc() |>
  st_zm(drop = FALSE, what = "Z")  |>
  st_as_text() |>
  stringr::str_replace('MULTILINESTRING Z', 'MULTILINESTRING M') |>
  st_as_sfc()

# result: XYM
x1
#> Geometry set for 1 feature 
#> Geometry type: MULTILINESTRING
#> Dimension:     XYM
#> Bounding box:  xmin: 0 ymin: 0 xmax: 1 ymax: 3
#> m_range:       mmin: 0 mmax: 0
#> CRS:           NA
#> MULTILINESTRING M ((0 0 0, 0 1 0), (1 1 0, 1 2 ...

# there it is, the M column
st_coordinates(x1)
#>      X Y M L1 L2
#> [1,] 0 0 0  1  1
#> [2,] 0 1 0  1  1
#> [3,] 1 1 0  2  1
#> [4,] 1 2 0  2  1
#> [5,] 1 3 0  2  1

# same for z dimension
x2 <- st_zm(x1, drop = TRUE, what = "ZM") |> st_zm(drop = FALSE, what = "Z")

#  result: XYZ
x2
#> Geometry set for 1 feature 
#> Geometry type: MULTILINESTRING
#> Dimension:     XYZ
#> Bounding box:  xmin: 0 ymin: 0 xmax: 1 ymax: 3
#> z_range:       zmin: 0 zmax: 0
#> CRS:           NA
#> MULTILINESTRING Z ((0 0 0, 0 1 0), (1 1 0, 1 2 ...

# and there is your Z
st_coordinates(x2)
#>      X Y Z L1 L2
#> [1,] 0 0 0  1  1
#> [2,] 0 1 0  1  1
#> [3,] 1 1 0  2  1
#> [4,] 1 2 0  2  1
#> [5,] 1 3 0  2  1

^{Created on 2024-04-24 with reprex v2.1.0}