I'm certainly not competing with the venerable and respected Rashi, but a half a century after making aliyah, moving to Israel, I definitely see a strong connection between Shmitta and Mt Sinai.
The connection between Shmitta and Mt Sinai is very simple. It's the paramount centrality of the Land of Israel to the foundation of Torah and Mitzvot. Since there are mitzvot that can only be observed in the Land of Israel, all Jews should be living here.
|Vayikra - Leviticus - Chapter 25|
on Mount Sinai: What [special relevance] does the subject of Shemittah [the “release” of fields in the seventh year] have with Mount Sinai? Were not all the commandments stated from Sinai? However, [this teaches us that] just as with Shemittah, its general principles and its finer details were all stated from Sinai, likewise, all of them were stated-their general principles [together with] their finer details-from Sinai. This is what is taught in Torath Kohanim (25:1). [And why is Shemittah used as the example to prove this rule, especially since the very fine details are not even specified here (Sefer Hazikkaron)?] It appears to me that its explanation is as follows: [At the plains of Moab, Moses reiterated the majority of the laws of the Torah to the Israelites before their entry into the land of Israel, this reiteration comprising most of the Book of Deuteronomy. Now,] since we do not find the laws of Shemittah [“release”] of land reiterated on the plains of Moab in Deuteronomy, we learn that its general principles, finer details, and explanations were all stated at Sinai. Scripture states this [phrase] here to teach us that [just as in the case of Shemittah,] every statement [i.e., every commandment] that was conveyed to Moses came from Sinai, [including] their general principles and finer details [and that the commandments delineated in Deuteronomy were merely] repeated and reviewed on the plains of Moab [not originally given there].
בהר סיני: מה ענין שמיטה אצל הר סיני, והלא כל המצות נאמרו מסיני, אלא מה שמיטה נאמרו כללותיה ופרטותיה ודקדוקיה מסיני, אף כולן נאמרו כללותיהן ודקדוקיהן מסיני, כך שנויה בתורת כהנים. ונראה לי שכך פירושה לפי שלא מצינו שמיטת קרקעות שנשנית בערבות מואב במשנה תורה, למדנו שכללותיה ופרטותיה כולן נאמרו מסיני, ובא הכתוב ולמד כאן על כל דבור שנדבר למשה שמסיני היו כולם כללותיהן ודקדוקיהן, וחזרו ונשנו בערבות מואב:
a Sabbath to the Lord: For the sake of the Lord, just as is stated of the Sabbath of Creation (see Exod. 20:10) [i.e., just as every seventh day is a holy Sabbath day, acclaiming that God Himself rested on the seventh day and thus acclaiming that God is the Supreme Creator of all existence, likewise, man must rest from working the land on the seventh year, for the sake of God, not for the sake of the land, so that it should gain fertility by lying fallow for a year]. — [Sifthei Chachamim ; Torath Kohanim 25:7]
שבת לה': לשם ה', כשם שנאמר בשבת בראשית: