It is well known that ר not lend itself to gemination. It never has virtual gemination. As for the full gemination indicated by the dagesh, ר allows it, but only very rarely, and never after the definite article. There are only about 15 words in Tanakh e.g. in 1Sam 10:24. I wonder if there has been an old tradition of articulation of the resh. Is it possible that the name שָׂרָ֖ה has once been spelled Sarra (and not Sara)? The famous pasuk Gen 17:15 is translated by the Septuaginta as follows:
וַיֹּ֤אמֶר אֱלֹהִים֙ אֶל־אַבְרָהָ֔ם שָׂרַ֣י אִשְׁתְּךָ֔ לֹֽא־תִקְרָ֥א אֶת־שְׁמָ֖הּ שָׂרָ֑י כִּ֥י שָׂרָ֖ה שְׁמָֽהּ׃
εἶπεν δὲ ὁ θεὸς τῷ Αβρααμ Σαρα ἡ γυνή σου οὐ κληθήσεται τὸ ὄνομα αὐτῆς Σαρα ἀλλὰ Σαρρα ἔσται τὸ ὄνομα αὐτῆς.
The Name Sara is transliterated Σαρρα and not Σαρα, whereas Sarai is transliterated with Σαρα. Any ideas?