We manage a multi-client google merchant center account.
For client X, we were admin of their Search Console.
When setting up their Google Merchant Center, I did verify it with their own Search Console, related to a different email.
I guess this is why their Google Merchant Center is not linked to our main multi-client account.
Also now our Search Console access is not verified.
If we delete the exiting verification code from the website and change it from the one in our previous Search Console, will this solve the issue? Would this change allow us to manage their account from our multi-client account?
When creating a new Google Merchant Center account for a client, should I create it with our own email then, and then give access to their email?
The easiest way to connect a GMC account to your multi-client Merchant account is creating it for your client inside your multi-client Merchant account and then giving them the access. If you need to gain access as multi-client account to already created account, you would have to contact Google support giving them the Merchant ID. The next step is that they send the owner an email that you are requesting an access and the owner has to confirm your access responding to that email. So the process is not impossible but it is much easier to create it for your client.
You can also verify the page using different options such as Google Analytics, Google Tag Manager etc. Changing the verification code might be a solution but it is hard to say because it might have influence on other services verified by the current verification code.