Halakhah הֲלָכָה

Hi again, Daniel!
The first mitzvah in Parashat Vayakhel is observing Shabbat and refraining from doing מְלָאכָה (melakhah, productive work). So this parashah provides another opportunity to explore Shabbat rules.
Last week, we discussed one aspect of melakhah in your question—that the mail is brought to you from outside the eruv. We saw that some rabbis thought you can’t benefit from this, and some think it’s okay.
Another potential issue is opening the mail, which might involve the melakhah of קוֹרֵעַ (korei’ah, tearing). But only certain kinds of tearing are forbidden.
Types of tearing
We learn from the Mishnah the general rule that tearing for תִּקּוּן (tikkun, fixing something) is not allowed on Shabbat, but tearing for קִלְקוּל (kilkul, destroying something) is less problematic (Mishnah Shabbat 13:3). Which one is opening mail?
This is a debate! According to some authorities, you’re allowed to tear open a letter because your tearing is kilkul—you are destroying the envelope (Haham Zvi 39, She’eilat Yaavetz 2:140). This is similar to a case in the Mishnah about breaking a barrel in order to eat what’s inside; it’s allowed, as long as you don’t intend to make a new object out of the newly opened barrel (Mishnah Shabbat 22:3).
Based on this, as long as you are not repurposing Devash’s plastic wrapping for some kind of creative project, you should be allowed to tear it open because it’s a case of kilkul. This is the same reason that you are allowed to tear open a bag of potato chips if you want to eat them on Shabbat, and tear the plastic wrapping off a new board game if you want to play it.
However, there is also a position that tearing open mail is a type of tikkun, because your ripping creates something new: access to the contents of the envelope. So, there are halakhic authorities who say that you should not open mail on Shabbat, unless there is a great need (Magen Avraham 307:20, Mishnah Berurah 340:41).