privacy of shipping labels when throwing packaging boxes away- what about prescription pill bottles?

when I order something from Amazon, the cardboard box comes with a label that includes my first and last name, exact address, city, and date that the delivery arrived

Should I worry about needing to shred/scribble out/censor personal information on these shipping labels before throwing away or recycling these packaging boxes?

What about labels on prescription pill bottles?

I know that a good majority of but NOT ALL labels on packaging boxes or prescription pill bottles are made of thermal …

address amazon box cardboard city delivery information name order packaging personal personal information privacy shipping