VSCE: lock down backwards compatibility in integration tests

[tjkandala]

We are aware that search doesn't work in the VS Code extension when it is pointed at a Sourcegraph instance that is <v3.31.2 (#31017). To better serve our enterprise users, we should ensure that the extension works for a (TBD) range of Sourcegraph versions while preventing regressions as teams make changes to core features.

• Determine the oldest version we should support
  • Depending on what version this is, it may involve additional work to get features working
• Ensure integration tests run against both the latest API version and the oldest version that we support (technical approach to be decided in PR)

[sourcegraph-bot-2]

Heads up @muratsu @jjinnii @ryankscott - the "team/integrations" label was applied to this issue.