I don't quit get this, but I saved the output of the wallet generated, including the private key which starts with 5 then I copied the wallet address P2SHAddress: 34VLvE2FRHwsmQLZ5jVG8shZWSyztpPn5d which was from the vanity output, and sent funds to it.
Are you sure the transaction has taken place? Can you check it on a block explorer? Use Tor if there's privacy concern. Is the destination the same as the vanity P2SH? Seems weird, and a reasonable explanation is that you just didn't send it to the same (e.g., due to trojan).
it shows the address format as BASE58 (P2SH), I don't have any other idea how to confirm if it is P2SH or legacy.
If it starts with 3 and it was generated by vanitygen, it's P2SH.