“The promised blessings are conditioned upon obedience”
Tou are confusing the Mt. Sinai convenant (which is conditional, as you correctly point out) with the convenant with Abraham (which is unconditional).
Paul teaches that it is Christians who inherit the Abrahamic promise.
"The promises were spoken to Abraham and to his seed. The Scripture does not say 'and to seeds,' meaning many people, but 'and to your seed,' meaning one person, who is Christ." (Galatians 3:16)
"If you belong to Christ, then you are Abraham's seed, and heirs according to the promise." (Galatians 3:29)