I have never also used Coinbase multi sig vault, through search I found out that you need to actual have some extended private key and if you have that then you can follow this guide to restore it in electrum https://bitcointalk.org/index.php?topic=2088713.msg20875786#msg20875786
The guide provided by Abdussamad in that thread won't help OP.OP should recover a 2 of 3 multi-signature wallet. That thread is about recovering a 2 of 2 multi-signature wallet and is not related to OP's issue.
The weird thing is there is no announcement from Coinbase that they are going to terminate Vault Wallet and honestly creating a Vault Wallet does not generate a private key it requires only 2FA and another email as co-signer.
See this: 
https://help.coinbase.com/en/coinbase/managing-my-account/other/the-multisig-vault
Coinbase multisig vault is 2 of 3 multi-signature wallet.
One of the keys is stored by the user, one of them is stored by coinbase and the user has no access to that. One of the keys (which is encrypted) is owned by both coinbase and user.
If you own two of the keys, you must be able to spend your fund without relying on Coinbase and without any need to 2FA or email verification.