Does the DROWN attack enable breaking strong RSA keys (e.g. the 2048-bit key itself) or enable breaking the plaintext (i.e. pre-master key) that is encrypted with a 2048-bit (or any strong) RSA, if the key is shared with SSLv2 server?
It breaks the secret key (master secret) that is encrypted using RSA; this secret key is the plaintext message; it is not the RSA private key.
Padding oracle attacks (DROWN uses a special form of the Bleichenbacher padding oracle attack) generally only attack the plaintext message, not the secret or private key used to create the ciphertext.