taking into account your visitors, in the normal case, the password change process should not require an interruption, meanwhile, in the production environment, you should apply it in the working time.
My suggestion is to apply this process first in Test, but in your case, the service account is the same in both environments, so you should worry about that.
Also, try to list all the application services, the application group, the Windows service, and the SQL services and make sure it is working and working after changing the password.
Here you can find all the possible problems that can face you and how to solve it. Password management for service accounts in SharePoint and SQL Server
The following are the necessary steps in the normal scenario:
Go to the Central Administration interface of SharePoint 2013, click on Security in the menu on the left and click on "Configure managed accounts". Select the farm administrators for the account in the list of accounts that is displayed, click on the Edit icon and change the password.
Manually change the password for the user profile service. As required by SharePoint, this service uses the farm administrator account, however, SharePoint 2013 does not treat this account as a managed account, so it must be changed manually.
Check if any of the applications in the secure storage service use the administrator account of the farm and if they change the password there.
Restart all servers in the SharePoint farm, except the SQL server. SQL Server does not need to be restarted.
For more details, see Step by step: changing the password for the SharePoint 2013 farm account