Prepare update for Turing v0.35

[penelopeysm]

TODO (in this order)

• [x] Release Turing 0.35.0 we're at 0.35.2 now
• [x] Bump min Julia version on intro page
• Verify that changelog is updated (Can't do this until it's merged)
• [x] https://github.com/TuringLang/docs/issues/521
• [x] Get rid of any other mention of Tracker, add Mooncake where necessary
• [x] Port #539

[penelopeysm]

Since 1.11 support is so hard (#560), I don't wonder if we could just stick to 1.10 for now.