Absolutely! The Lievito Madre from Bakeing Warehouse is a good example, you can just bake with it, or use it as a wheat sourdough kick starter. Making Lievito Madre DIY is tricky, rye is much simpler.
My rye starter is now 2.5 years old, but just for safety I dried some and keep it as backup in the fridge. This dried starter can keep forever and you can use it to kickstart in case something goes bad with the every day starter.
Not sure about the Tesco one though. It can have real sourdough in it, or just sourdough taste from dead sourdough. The recipe should tell, living sourdough would take a few hours longer. (btw bread usually does not contain butter)
https://www.bakingwarehouse.com/prod...d-mother-yeast