In Birkat Hamazon, we (Ashkenazim...I haven't looked at other texts) add a line on Shabbat, "הַרָחֲמָן הוּא יַנְחִילֵנוּ יוֹם שֶׁכֻּלוֹ שַׁבָּת וּמְנוּחָה לְחַיֵּי הָעוֹלָמִים" which translates to "May the Merciful One let us inherit that day which will be all Shabbat and rest for life everlasting. "
This concept seems to stem from the Mishna in Tamid (7:4, or 6:7) which focuses on the Shir Shel Yom and says that the song the Levi'im sang on Shabbat was "מזמור שיר, ליום השבת" (תהילים צב,א)--מזמור שיר לעתיד לבוא, לעולם שכולו שבת מנוחה לחיי העולמים. " (though I am ignoring the addition of the vav before m'nucha in the version used for bentching)
The Kehati comments "The Shabbat of God is the seventh millenium..." as a day is equal to a thousand years and the Bartenura further connects the idea to the Zoharic notion that God will be alone in the universe for a millennium (" ועל שם שבאלף השביעי לא יהיה כי אם הקב״ה,") and, according to my English text, "the world will be entirely in a state of Shabbat rest." The Yachin (from sefaria.org) provides 3 possible understandings including mentions the destruction of the world which is then rebuilt by God (לאחר שיחרב העולם בסוף אלף הששי, אשר אז ינוחו כל חיי העולמים כולם אלף שנה, עד שיחזור הקב"ה לבנות אח"כ העולם מחדש) , and also the idea of a separation of body and soul ( חיי עה"ב אחר פרידת הנפש מהגוף).
Are we then asking for a time when we do not exist? In what way will there be "rest" if there is no person around to do "work"? Wasn't Shabbat a special sign between God and the Jews? What value would there be if there were no Jews? But if this isn't about a time bereft of humanity, will this time be one when the LAWS of Shabbat will hold sway for the reincarnated people or will it simply be the seventh in a cycle?