Paul is drawing a parallel between the our bodies and the ground (from which we are formed), which both "groan" in hope to be liberated from the curse of Adam.
When Paul says that the whole creation "suffers the pains of childbirth" (Rom 8:22), he is making a direct reference to the sin of Adam, which precipitated the curses from God (that included the suffering in childbirth for the woman). That is, the ground had received the curse when Adam sinned (Gen 3:17-19). This curse is why our bodies suffer decay and return to the dust, because we are formed from the ground, to which we return: "ashes from ashes, dust to dust" (Gen 3:19).
But there is a new birth around the corner, and the labor pains of the creation are in hope for this time when the curse on the ground will be lifted. Paul calls this time when "the creation will be set free from the corruption into the freedom of the glory of the children of God" (Rom 8:21).
For example, when the ground "groans and suffers" (earthquakes, tsunamis, volcanoes, etc.) the cause is the curse that stemmed from the sin of Adam according to Romans 8:20-22. These groanings are the labor pains of the new birth, when one day the ground will be set free from the curse of the ground. In other words, Paul indicates that there is a HOPE that one day in the future that the curse would be lifted from the ground. This HOPE is why the ground "groans." The curse on the ground causes the "groans and suffering" (Rom 8:22), but the "groaning" also stems from the hope of the new birth (release from the curse of Adam) according to Romans 8:23. Or to put it another way, the curse of Adam causes "groans and suffering for the whole creation," but the HOPE of the release from the curse of the ground (for both earth and the Christian) is the reason that we "groan." So while suffering is mitigated, there is still this groaning that remains.
LIKEWISE (Ὡσαύτως), we too will be set free from the death and decay of our bodies, and so we have the hope of "release from the corruption into the freedom of glory..." (Rom 8:21). Our physiological groanings however are not earthquakes, tsunamis, volcanoes, etc., but IN LIKE MANNER (Ὡσαύτως) and in parallel with the earth, the groanings come from within "deep." The Spirit of God articulates these "deep" groanings and intercedes our suffering to the Father in heaven (Rom 8:26), but in hope. This "hope" is this future day for which the ground yearns (Rom 8:20-21), and for which we look forward to the redemption of our bodies from corruption according to Romans 8:23.
In summary, what throws us off and confuses us in this passage is that groaning occurs within suffering because of the sin of Adam and its attendant curse on the creation (thus groaning and suffering happen together). But because there is this hope of release from the curse on the creation, the groaning (in the ground and within our bodies) is actually stemming from the hope of the release from the curse on the creation. This groaning is akin to labor pains, which happen before the new birth (release from the curse). Thus within suffering there is hope, which causes the "deep" groaning.
This slight nuance of meaning and parallel is why we can slip and miss the meaning of this passage.