Debt - Transition off of Tokio 0.1

[vector-vic]

This is the big one. We need to keep up with the ecosystem here to avoid becoming blocked on upgrading important dependencies.

Goal

Our goal should be to set ourselves up for easy, incremental change. Currently, we have some futures 0.3 code that we map back to futures 0.1 via the compat layer. Success here means flipping that around. We'll still have plenty of futures 0.1 code, but it should be compat-mapped into futures 0.3, which is then the default for all new code.

Actually moving totally to futures 0.3 will be a long, incremental journey. This piece of work should lay the foundation and plot a rough course.

Plan of Attack

1. Investigate and clear potential blockers (#1695, #1696)

2. Make the minimal change onto tokio-compat as described in #1142

3. Test heavily

4. Triage existing futures 0.1 code

Other related issues: #1639, #716, #990

[vector-vic]

Link to feature: https://timber.productboard.com/feature-board/planning/features/5156388

[binarylogic]

Nice work @kirillt! Really awesome to see this completed.