Our World in Data provides a chart showing municipal waste recycling rates for 38 different countries and regions. I've selected the available EU countries here:

(EU countries missing from this chart are Bulgaria, Croatia, Cyprus, Malta, and Romania.)
The data source is the OECD's statistics on municipal waste, generation, and treatment where you can find data through 2020 for several countries, as well as additional data points on composting, incineration, and a few categories of waste.
To your question about recycling rates of specific materials (such as glass), I only know of one for metals: the UN Environment Program 2011 report, Recycling Rates of Metals. A google search indicates there may be some reliable resources available for glass as well, but I am not familiar with any of them in particular.