Just to clarify a couple points:
It is not the MySQL databases that are being deprecated. It is the MySQL drivers that are used by the PHP application to connect to the database.
They are being replaced by a new set of drivers, MySQLi. This deprecation has nothing to do with the database end, it has to do with the PHP application server and how it connects to databases.
Existing applications that you have developed will continue to work as long as the host is using a PHP version that is compatible with the MySQL drivers.
Any hosts that I have dealt with will allow you a way of selecting which PHP server version to use. in 1&1 I can select to use v4.2 as an example.
The Switch to MySQLi is for future versions of PHP where the MySQL drivers will no longer be available. We will be upgrading Data Bridge, eCart, and Design Extender to offer support for MySQLi in the near future, those upgrades will offer support for both MySQL in order to maintain old projects and MySQLi for new projects.