Upgrade `analytics-node` npm package

## Overview
`analytics-node` is the Node.js package for Segment analytics.

The current version we're running (3.4.0-beta.3) is 2 years old and is no longer being maintained as of 8/31/22. It also uses Analytics.js 1.0. Segment has been on Analytics.js 2.0 for some time.

The latest package version is 6.2.0 released on Aug 2, 2022.

https://github.com/segmentio/analytics-node/tags

## Breaking Changes During Upgrade
For full changelog, see https://github.com/segmentio/analytics-node/blob/master/History.md

3.4 -> 4.0
BREAKING: throws error when message is over 32kb #268

4.0 -> 5.0
BREAKING: Dropping support for Node 8.0!

5.0 -> 6.0
Breaking: Flush now properly returns a Promise #288


Start by locating the current analytics-node dependency declaration and its call sites in the repository. Read the linked History.md, paying particular attention to the listed breaking changes, then run the relevant repository checks after upgrading; done means the package is on 6.2.0 and existing analytics behavior remains working.

Written by the indexing model from the issue text.