Bart writes
Does anyone have any idea when South West Trains at Waterloo will be
able to start issuing season tickets on Oystercard?

Not for a long, long time.

At present, you can only buy monthly and annual cards from the website.
Once this part of the 'public trial' is complete, they will be adding
weeklies, stored-value and LU stations/pass agents. I reckon NR
stations will be the last to offer Oyster (if at all).

--
Dave