Having backups for your wallet is good but it is not enough. You must do two other important things
1. Keep your backups safely from others to avoid risk that they will steal it (if they are greedy) or throw it away (because they did not know importance of that piece of paper).
2. Make sure you assign a place for your backup storage and it's always in your mind. In case there is emergency, you can quickly know where it is and can take it to run away.
You are fortunate to have located the backup, if one of your friends who is knowledgeable about cryptocurrency had been in your room and discovered the backup, or if the garbage had already been disposed the situation might have been quite different. Nobody can be trusted, especially when it comes to money, so you shouldn't be careless with your backups. In fact, you shouldn't even keep them in a place where a second person could possibly see them. Once, I was about to secure my backup then I exited the room and left it on the table. When my little sister entered my room, she just happened to notice it and torn it to pieces. I was lucky to have another copy of it else I would have lost my asset.
It's the same as what happened to me the only difference is that you are lucky that you still find the paper backup in the garbage compared to mine where they already burned my backup paper.
That is why I decided to put all paper backups in a storage box that includes my important documents and I told them not to touch my storage box without my permission.
Not everyone is lucky though, i am sure you learn from your mistake just as i did. Keeping your backup in a storage box is good but it’s advisable to make duplicates and store in a separate location in case of any unforeseen circumstances.
One of the best ways to secure the wallet recovery phrase is to have multiple backups of it in at least two places.
One is for urgent use and writing it on paper will do. The second copy should keep in a safety deposit storage or box to avoid losing the fund during a disaster. An example is the heartbreaking issue that happened in Turkey and I am sure a lot of Bitcoin holders that escape the accident would lose their wallet recovery phrase.
That was a horrible incident lots of lives were lost. We will keep praying for the lives lost and the family of those who lost their loved ones to the disaster. We don’t pray to experience such again but that is one of the reasons why you should have multiple locations for your backups.