There is a מנהג in כלל ישראל to put non-bearing fruit trees in shuls on שבועות because on עצרת the judgement for the upcoming year’s fruit tree is decided (מג"א או"ח ס' תצד ס"ק ה). There are two questions that can be asked. Firstly, if we are judged in regard to fruit bearing trees, why do we put non fruit bearing trees in shul? Secondly, why is it that on ט"ו בשבת which is ראש השנה לאלנות do we celebrate by eating fruit and not with trees, an on שבועות which we are judged for the upcoming year’s fruit do we celebrate by putting trees in shuls, it should be the opposite?
When אדם הראשון sinned and was punished, the ground was also punished because it did not produce trees that tasted like its fruit. The fact that some trees don’t produce fruits can be understood as an extension of this punishment. In fact, in the beginning of פרשת בחקותי, on the Pasuk “ועץ השדה יתן פריו”, Rashi says it is referring to non-bearing fruit trees which will produce fruits in the future.
קבלת התורה was a תיקון for the חטא of אדם הראשון because the idea behind the sin was not wanting to take responsibility for ones actions, as we see from his response to Hashem האשה אשר נתתה עמדי הוא נתנה לי מן העץ ואכל. However, when the Jews were מקבל the torah at הר סיני, it was an acceptance of responsibility that we understand that our actions have consequences and ramifications and we are willing to take אחריות for our actions. This idea is also reflected in the Zohar. The Zohar says that the זוהמא that came into the world by the חטא of אדם הראשון was פסק at הר סיני (temporarily) and it was a moment of אדם הראשון קודם החטא . Therefore we specifically put אילני סרק in shul on שבועות because קבלת התורה was a תיקון for the חטא of אדם הראשון which also included the חטא of the אדמה that it produced trees that didn’t have טעם פרי and trees that did not produce fruits. This also answers the second question because with the תיקון of for the חטא of the אדמה, trees will revert back to tasting like their פרי. Therefore we put trees in shuls even though עצרת has to do with fruits because with the תיקון, trees will be like the fruit itself.