Remove the use of `fuchsia.deprecatedtimezone`

[filmil]

This is related to issue #39174.

Now that we've removed the use of fuchsia.timezone, we're on to removing the uses of fuchsia.deprecatedtimezone. I'll be working on this, and unless someone else is really eager to take it over, you can expect a pull request from me soon.

[filmil]

Reviewed at: https://dart-review.googlesource.com/c/sdk/+/129005