I am sharing my solution in case it helps anyone.
It provides the info needed to implement the use case of the question and also avoids infinite recompositions by following the recommendation of https://developer.android.com/jetpack/compose/lists#control-scroll-position.
- Create these extension functions to calculate the info needed from the list state:
val LazyListState.isLastItemVisible: Boolean
        get() = layoutInfo.visibleItemsInfo.lastOrNull()?.index == layoutInfo.totalItemsCount - 1
    
val LazyListState.isFirstItemVisible: Boolean
        get() = firstVisibleItemIndex == 0
- Create a simple data class to hold the information to collect:
data class ScrollContext(
    val isTop: Boolean,
    val isBottom: Boolean,
)
- Create this remember composable to return the previous data class.
@Composable
fun rememberScrollContext(listState: LazyListState): ScrollContext {
    val scrollContext by remember {
        derivedStateOf {
            ScrollContext(
                isTop = listState.isFirstItemVisible,
                isBottom = listState.isLastItemVisible
            )
        }
    }
    return scrollContext
}
Note that a derived state is used to avoid recompositions and improve performance.
The function needs the list state to make the calculations inside the derived state. Read the link I shared above.
- Glue everything in your composable:
@Composable
fun CharactersList(
    state: CharactersState,
    loadNewPage: (offset: Int) -> Unit
) {
    // Important to remember the state, we need it
    val listState = rememberLazyListState()
    Box {
        LazyColumn(
            state = listState,
        ) {
            items(state.characters) { item ->
                CharacterItem(item)
            }
        }
        // We use our remember composable to get the scroll context
        val scrollContext = rememberScrollContext(listState)
        // We can do what we need, such as loading more items...
        if (scrollContext.isBottom) {
            loadNewPage(state.characters.size)
        }
        // ...or showing other elements like a text
        AnimatedVisibility(scrollContext.isBottom) {
            Text("You are in the bottom of the list")
        }
        // ...or a button to scroll up
        AnimatedVisibility(!scrollContext.isTop) {
            val coroutineScope = rememberCoroutineScope()
            Button(
                onClick = {
                    coroutineScope.launch {
                        // Animate scroll to the first item
                        listState.animateScrollToItem(index = 0)
                    }
                },
            ) {
                Icon(Icons.Rounded.ArrowUpward, contentDescription = "Go to top")
            }
        }
    }
}
Cheers!