Sorry for the delay.
The query in the first JPG (Alter Add Table) returns 1 correctly, this is the result of the last statement, the last statement is ALTER TABLE, it returns either success or failure, 1 is success. The computed fields do not work because the second coordinate system passed to the converter is wrong: you are calling ComponentCoordSystem on a table, the table may have multiple geometry or tile fields, it does not have a coordinate system as a whole. You should have called ComponentCoordSystem on the drawing.
(1) Since you said earlier that you already see the desired lat/lon values in the Info pane, you don't need to convert coordinate systems, you can use the value of the 'Geom' field without conversions.
(2) If all you are interested in is points, you don't need GeomCenter or GeomToCoords either, you can just take the geom and get its first coordinate using GeomCoordXY.
SELECT [Point Number],
VectorValue(GeomCoordXY([Geom], 0), 0) AS [Lon],
VectorValue(GeomCoordXY([Geom], 0), 1) AS [Lat]
FROM [Points Lats Long Drawing 2];
If you want to be able to access that as computed fields, here's an adaptation:
ALTER TABLE [Points Lats Long Drawing 2 Table] (
ADD [Lon_n] FLOAT64 AS [[ VectorValue(GeomCoordXY([Geom], 0), 0) ]],
ADD [Lat_n] FLOAT64 AS [[ VectorValue(GeomCoordXY([Geom], 0), 1) ]]
I used 'Lon_n' / 'Lat_n' because 'Lon' / 'Lat' were already taken. If you want to limit the number of decimals, use RoundDecs (we will make this unnecessary in the future by letting you control the output style for a field). If you want to allow lines / areas / multipoints, add GeomCenter. If you want to use a different coordinate system than the one used by the geometry values, add coordinate converter (see code from steveFitz).