Is it correct to write "رضني" (radini) in the Istikhara supplication, or should it be "أرضني" (ardini), or is "رضّني" (raḍḍini) with a shaddah on the ḍād intended?

Both narrations are correct. The hadith has been transmitted with the wording "thumma arḍinī bihi" (then make me pleased with it) and with the wording "thumma raḍḍinī bihi" (then make me pleased with it) with a shaddah on the ḍād. Both are correct, and Al-Hafiz said: "Then make me pleased (raḍḍinī) with a shaddah, and in the narration of Qutaybah, 'then make me pleased (arḍinī) with it,' meaning make me content with it."