chore(cli): migrate @fern-api/register to use CliError

[FedeZara]

Description

Migrates @fern-api/register to use explicit CliError error codes on every failAndThrow / failWithoutThrowing call site.

This is one of the package migration PRs that follow the error classification system introduced in #14749.

Changes Made

Assigned typed error codes across call sites in packages/cli/register/src/.

Error codes used

Code	Usage
NETWORK_ERROR	API registration failures, server communication errors
AUTH_ERROR	Authentication failures during registration
CONFIG_ERROR	Invalid registration configuration

Files touched (grouped by area)

• Registration: registerApi.ts

Testing

• Existing tests pass (pnpm test, excluding e2e and pre-existing environment failures)

[FedeZara]

• chore(cli): migrate @fern-api/register to use CliError #15008 👈 (View in Graphite)
• main

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