Clean-up any deprecated code not needed after migration to use apiclient.Client

[alexec]

Summary

What change you think needs making.

Motivation

To reduce tech-debt and provide a Golang client for external users.

Depended on by #1951.

Proposal

Please speak to @alexec about how to do this. You'll probably need to write new e2e tests, and as a find bugs you need to fix. You should be able to find where you need to make changes based on //DEPRECATED.

• client/conn.go
• common.go

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