Complete statistics tracking

**Task description**: Right now, the statistics system for loading/saving is complete. However, only the "time played" statistic is currently tracked. Therefore, we need to complete those statistics as well.

_Anyone can feel free to contribute on a smaller or larger portion of this task as they feel. There is no absolute need to complete all of the following in one PR. Hop on the [Discord channel](https://discord.gg/TFJqhsC) to have a chat with other contributors._

_If you plan on working on this task, please feel free to let us know in the comments. If you plan on working on a larger portion of the task, please open a Work In Progress Pull Request so we can track this issue._

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**Statistics to track**
- [x] Games quit
- [x] Time since last death
- [x] Sneak time
- [x] Distance walked
- [x] Distance crouched
- [x] Distance sprinted
- [x] Distance swum
- [ ] Distance fallen
- [x] Distance climbed
- [x] Distance flown
- [ ] Distance dove
- [ ] Distance by Minecart
- [ ] Distance by Boat
- [ ] Distance by Elytra
- [x] Jumps
- [x] Items dropped
- [x] Damage dealt
- [x] Damage taken
- [x] Number of deaths
- [x] Mob kills
- [x] Animals bread
- [x] Player kills
- [x] Droppers opened
- [x] Hoppers opened
- [x] Dispensers opened
- [x] Chests opened
- [x] Furnaces opened
- [x] Crafting tables opened
- [x] Ender chests opened

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Start by locating the existing statistics loading, saving, and time-played tracking code. Compare its behavior with the unchecked statistics in the issue, then determine how each missing statistic should be updated and persisted. Done means the listed missing statistics are tracked consistently with the existing system and survive loading and saving.

Written by the indexing model from the issue text.