[Persisted tab data]Implements the non-deprecated builder.

Any class inheriting `BrowserContextKeyedServiceFactory` should
implements either `BuildServiceInstanceForBrowserContext` or
`BuildServiceInstanceFor`. The second one being deprecated,
this CL replaces it by the first one.

This also ensures that, instead of applying `WrapUnique` to a `new` raw
ptr, it directly uses `make_unique`.

Change-Id: I25b085ba6bc10d4059e2ef9d2e1547e54a78488d
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4799870
Reviewed-by: David Maunder <davidjm@chromium.org>
Commit-Queue: Arthur Milchior <arthurmilchior@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1376892}