Why can't I see application changes made in previously published sandboxes in my current sandbox?

That's because a sandbox is set to only one context layer, and layers are applied in a specific order.

Applied 4^th: User
Applied 3^rd: External or Internal
Applied 2^nd: Job Role
Applied 1^st: Site

When you're in a sandbox set at a specific layer, you can see your own changes plus changes from previously published sandboxes that were set at your context layer and below it. You won't see changes made in previously published sandboxes if those sandboxes were set at a layer that's higher in the hierarchy. So while working in your sandbox, what application changes you see depend on these factors:

The layer at which changes were made in the previously published sandboxes
The layer activated in your sandbox

However, you can switch to preview mode to test your changes alongside changes made in previously published sandboxes at all layers. Preview mode puts your sandbox into a read-only mode, where you can see all changes, including those made at a layer higher in the hierarchy than your own. After testing and validating your changes in preview mode, you can publish your sandbox.

Let's look at a few examples to understand how context layers impact what changes you can see in your sandbox:

When working with Application Composer in a sandbox, your sandbox is always automatically set to the Site layer. In this sandbox, you can see your own changes plus any previously published configurations made at the Site layer. But you won't see changes that were made at higher layers, such as Job Role, External or Internal, or User.
Let's say you're working with Page Composer in a sandbox at the Job Role layer. You can see your own changes plus changes made in previously published sandboxes at the Site and Job Role layers. But, perhaps in that sandbox at the Job Role layer, you hid a page component and published your changes. Now, if you create a sandbox for Page Composer at the Site layer, you will still see that page component (it's not hidden!) because Site is lower than Job Role in the hierarchy. The changes made at the Job Role layer won't reflect in your sandbox at the Site layer, unless you switch to preview mode.