Adding table to layout using PyQGIS

Question

I need to create a table based on a Python list and paste it in layout view in QGIS.

I also found a QgsLayoutTable class in PyQGIS but there's no example of creating a simple table.

If I had these objects:

layout = QgsProject.layoutManager().layouts()[0]

table_data = [
  ["a", "b"],
  [1, 2,
]

How could I create a QGIS layout table like

a	b
1	2

and add it to the layout?