The Following is from the Gevuras Yitzchak on Bein HaMitzarim:
The Shulchan Aruch tells us that we refrain from making the bracha of Shehecheyanu during the 3 weeks. The Magen Avraham asks why this is so, we do not see that an avel can’t make a shehecheyanu. Therefore, we must say that it is the time period which is not conducive for the making of this bracha. However, on Shabbos one can make the bracha. Since the applied reason is the nature of this time period, why is it permitted on Shabbos?
The Gemarra in Gitten explains that the satan has no power in causing machlokes on Shabbos. The Maharal says that Shabbos is Sheleymus (may’ein olam haba), and machlokes is the opposite of sheleymus. We also see the Torah was given on Shabbos due to the Shleymus and achdus involved. Shabbos enabled Klal Yisroel to reach a level of Sheleymus and Achdus.
The Gemarra in Yuma explains that the 1st Beis HaMikdash was destroyed due to the “big three” (murder, idolatry and adultery) and the 2nd Mikdash was destroyed due to sinas chinam. From here we can see that sinas chinam is at least equal to the “big three”. Rabbeinu Yona says that sinas chinam leads to loshon hara and the Chofetz Chaim says, that despite the gemarra mentioning sinas chinam, the gemarra is really referring to loshon hara.
The Yerushalmi Yuma explains the events of Bais Sheini. Since the people at that time they loved money, they developed a jealousy towards one another, which gave birth to sinas chinam and machlokes in Klal Yisroel.
Now we can see why we have the aforementioned din in regards to Shehecheyanu. It has nothing to do with mourning. Since the jealousy of a new item can possibly lead to the sinas chinam and lashon hara which destroyed the beis hamikdash, we will refrain from acting in a way which could spark this jealousy. However, on Shabbos, which is itself Shelaymus and which enables Klal Yisroel to reach great levels of achdus, one need not be worried.
(I hope I said this clearly, I can restate things if unclear)