Way to fetch vault id by wallet address?

Is there a way to fetch vault id just by a given wallet address?

Yes. Fireblocks now provides a reverse-lookup endpoint for this:

GET /v1/vault/lookup_by_address?address=<BLOCKCHAIN_ADDRESS>

The response includes the owning vaultAccountId and the blockchains associated with the address.

Java:
fireblocks.vaults().lookupVaultByAddress(address);

The endpoint is currently marked as beta. A 403 means the feature is not enabled for the workspace, while a 404 means no owning vault account was found.