Update JobCoordinator remaining methods to be shard aware

What does this MR do and why?

This MR wraps Sidekiq APIs with Sidekiq::Client.via to achieve shard-awareness in a sharded Sidekiq context. This does not affect self-managed (SM) users or .com at the moment since the sharding feature is behind a feature flag enable_sidekiq_shard_router.

Uncovered in !149648 (closed)

See issue: gitlab-com/gl-infra/scalability#2817 (comment 1864874290)

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