Sforno on Exodus 16:27/ספורנו על שמות ט״ז:כ״ז

1יצאו מן העם, from their camp to the area where during the week the manna had been falling. These people thought that they would find some manna, possibly outside the usual parameter. This was a demonstration of lack of faith in the word of G’d.

2ללקוט, this would have been an outright desecration of the Sabbath. Even carrying their containers was a desecration of the Sabbath. The Talmud Shabbat 107 states that even something only peripherally attached to the ground, i.e. something which had not actually had grown in the earth, had roots, is nonetheless considered halachically as if it had been uprooted from the soil.