Can tested yeast be used for anything? I tested my yeast using the method explained on this video: https://youtu.be/p8ydC1Of_Zw (go to 2:05 min)
Here is the method in case you can't access the video:
1) dissolve 1 tbsp of sugar in half a cup of warm water
2) add 2 and 1/4 tsp of dry yeast and stir
3) wait 10 min
4) if foam rises to 1 cup mark yeast is good. Otherwise it's not.

It turned out to be good.

I don't like to waste food or ingredients, so I was wondering: can I now use that mixture instead of yeast in any recipe that requires yeast? Can I use it in place of a sourdough starter maybe?

If yes, how can I best store it to save it for future recipes?

Thanks
You can certainly use it immediately in the place of yeast in a recipe - you basically have done a pre-activation of the yeast. This is a common part of many recipes.

You should also be able to store it in the fridge for at least a few days and then add it to a bread recipe without any problems. Yeast are quite hardy and will survive fairly well over that time.

You could also dry it down in parts onto sheets of foil, wrap them up and use them to inoculate a new mixture, you can then expand this mixture to propagate them indefinitely - free yeast!