Hello Sumaira,
I strongly advise that you have a look at the Unified Interface various Playbooks that contain a lot of information on Unified Interface.
The first 2 chapters present the Unified Interface and how to quickly test it (as you mentionnes, by enabling the "Unified Interface Only" mode on a sandbox.
Chapter 3: Transition is especially focus on switching to the Unified Interface: https://docs.microsoft.com/en-us/powerapps/maker/model-driven-apps/unified-interface-playbook
Instead of just switching on the "Unified Interface Only" mode, I suggest that you adopt the Unified Interface either by using the Microsoft first-party apps (e.g. Sales Hub, Customer Service Hub, etc. - that can also be customized) or create your own new model-driven apps that will allow you to offer role-based experiences for your users (so for example a salesperson sees different navigation, dashboard, views, forms, etc. than a customer service person would. Simply create one a app per role, associate relevant security roles with these apps, and hand-pick what they should see).
Now in regards to the email you have received: it means that we encourage you to validate a transition date. But if you are not confortable with the date or would like more time, you can request a different one, or simply not approve the date. In that case, when the initial proposed date passes, we'll suggest a new one, and we'll do this until October 2020, when the legacy web client will not be available anymore.
If you haven't customized your application with unsupported or deprecated methods, the system should still work in Unified Interface, but we still strongly advise that you test your business scenarios. In any case, the data will not change at all, as all that changes is the user interface rendering.
Henry
