Carrots and Dorot Products during Shemitah

Answer

 Dorot carrots are heter mechirah.

Expanded answer:

Kibbutz Dorot is near Sederot (5 km SE) in the Sha'ar HaNegev Regional Council and is supervised by the Sederot Rabbinate. The carrot factory has recently (Iyar 5782, May 2022) closed. Dorot Farm no longer exists in Israel.

On imports: Dorot transferred its franchise (Dorot Farm) to a company that exports other Israeli carrots to the North American markets: Gezer Shluhot and other carrot producers, all sold under the Dorot Farm brand. The kibbutz notified all kashrut agencies, including Badatz agencies, about this move.

I received this information from Eliyahu Tal, 050-5239031, 08-6808714, on the Sederot Rabbinate website. Rabbi Ari Sat, Rabbi of Kibbutz Sa'ad, said that to the best of his knowledge, carrot production is heter mechirah (with the exception of some in Alumim, which is in olei Mitzrayim territory and is sold by Otzar Ha'aretz; carrots are not grown in the Aravah).

To the best of my knowledge, all farmers in Israel produce carrots (let alone import them) through heter mechirah.

Carrots can technically be stored for more than six months. However (as of Iyar 5782), as far as I checked no sixth-year carrots are left or being sold by any company.

Dorot beets are also heter mechirah.

Dorot's spices are certified by Rabbi Efrati's Badatz. There are large quantities still left from the sixth year and herbs are also grown in the southern Aravah under Rabbi Efrati's guidelines. To the best of Eliyahu Tal's knowledge, there is no yivul nochri for spices.

Garlic is imported, apparently from China.

According to Rabbi Ari Sat, the place where carrots are grown is not necessarily the same place it is packaged. For instance, Gezer Shluhot buy their carrots from carrot growers in other locations. The carrot factory in Sa'ad also buy carrots from growers all over Israel, not necessarily only from Sa'ad or the surrounding kibbutzim.