New table containnig objects in a [List]

If you have tableX that looks something like...

You can get a tableY that looks like...

with the following code...

let
    Source = tableX,
    #"Expanded Object" = 
    Table.ExpandListColumn(
        Source, 
        "Object"
    ),
    #"Added Index" = 
    Table.AddIndexColumn(
        #"Expanded Object", 
        "tableY ID", 
        1, 
        1, 
        Int64.Type
    ),
    #"Added Prefix" = 
    Table.TransformColumns(
        #"Added Index", 
        {{"tableY ID", each "ID_" & Text.PadStart(Text.From(_), 4 - Text.Length(Text.From(_)), "0"), type text}}
    ),
    #"Reordered Columns" = 
    Table.ReorderColumns(
        #"Added Prefix",
        {"tableY ID", "tableX ID", "Object"}
    )
in
    #"Reordered Columns"

If you did not want tableX IDs with no objects in their list to get a tableY ID you would need to add a step after 'Expanded Object' that filters out those rows (null rows).
Hope this gets you pointed in the right direction.