Luggage transfers in Switzerland

SBB does have luggage service, but I don't think they have same-day guarantee. Info here.
https://www.sbb.ch/en/station-services/services/luggage/luggage.html

I don't think they have this service to Salzburg, Austria. Just selected stations in Germany.
Most larger and medium Swiss stations have luggage lockers. Check at individual stations.
https://www.sbb.ch/en/station-services/railway-stations/further-stations.html

Yes, it is available between major (manned) stations only.
There is a door-to-door service at extra cost, so you don't have to go to the station to pick up your luggage.

Can it be sent on the same day that we board the train and be available for pick up at the same time when we get to our destination?

No, it does not travel on the same train as you. "Drop off your luggage today and collect from your destination station the day after tomorrow."

Details here: https://www.sbb.ch/en/station-services/services/luggage/luggage.html

Can the luggage be sent from a city in Switzerland to Austria e.g. Konstanz to Salzburg.

There is a service to Germany only, not to Austria.
But, Konstanz is not in Austria, it is in Germany. For the German service "Drop off your luggage by 7 p.m. today and collect it a couple of days later from your destination address in Germany."

The station-to-station service options used to be faster, but they changed in (I think) June, 2018. The door-to-door service has an express option, but with extra fees both for door-to-door and for express (which apply per group, not per bag).