There won't be readily available and easily digestible English sources for these topics but... ~20% of total wastes are recycled[0], of which:
- 86% of plastics are "recycled", of which 56% is "thermally recycled", the rest 25% is only quoted as "chemical recycling and material recycling combined" in most PR materials, which I think is enough indication that it's not going back into bottles.[1][2]
- I was wrong about glasses: 70% of glass bottle source materials comes from recycled materials[3], and use of reusable bottles have declined over the years and converging into 50%[4](by numbers of bottles?).
- Papers and milk cartons[5] are fine as had always been; I think those were recycled to toilet papers.
... but the bottom line is 76% incinerated, 1% buried[0], rest recycled of which major part is by "thermal" means. So most of it is burned. Personally I think there won't be rapid drastic changes in this front and it's possibly more worthwhile to find green sources of plastics such as grain straws and fruit skins(but I think I did see a lot of such presumably failed attempts at it in the past couple decades)