This is what I did to get the width the same as the text field: Copying and modifying Gabriele's answer.

var expanded by remember { mutableStateOf(false) }
val suggestions = listOf("Item1","Item2","Item3")
var selectedText by remember { mutableStateOf("") }

var dropDownWidth by remember { mutableStateOf(0) }

val icon = if (expanded)
    Icons.Filled.....
else
    Icons.Filled.ArrowDropDown


Column() {
    OutlinedTextField(
        value = selectedText,
        onValueChange = { selectedText = it },
        modifier = Modifier.fillMaxWidth()
            .onSizeChanged {
                dropDownWidth = it.width
            },
        label = {Text("Label")},
        trailingIcon = {
            Icon(icon,"contentDescription", Modifier.clickable { expanded = !expanded })
        }
    )
    DropdownMenu(
        expanded = expanded,
        onDismissRequest = { expanded = false },
        modifier = Modifier
                .width(with(LocalDensity.current){dropDownWidth.toDp()})
    ) {
        suggestions.forEach { label ->
            DropdownMenuItem(onClick = {
                selectedText = label
            }) {
                Text(text = label)
            }
        }
    }
}