This is an initiative to bring retention policies of all products at one place. The new Exchange Admin Center, doesn't have Microsoft 365 compliance center for Exchange security and compliance features. So, you may see the features in old admin center only. A single mechanism to centrally manage both retention and deletion of content across Microsoft 365 is a good idea going forward.
To answer the questions
- If I want to hold/retain Teams chat - either private or channel - do I need to configure the Compliance policy? Or is this held already as part of in-place archive?
Yes. You should create it separately as the compliance policy available at Exchange control panel is not used by Teams. - In fact do I need to configure retentions for all areas at all?
It's a good idea to create policies for each product from the new interface. You can't use single policy created here for multiple products. So create separate policies for Teams and Exchange - retention