Recycling works very well for some materials and poorly for others, and the difference is chemistry and economics rather than effort.
What recycles well
Aluminium. Melts down with almost no loss of quality, indefinitely, using a fraction of the energy of primary production. The most successful recycling there is.
Steel, similarly, and it is magnetic so separation is easy.
Glass, which melts and reforms repeatedly, though colour mixing limits what it can become and the weight makes transport a large share of the cost.
Paper and cardboard, though fibres shorten each cycle, so it can be recycled perhaps five to seven times before the fibre is too short.
What does not
Most plastics. There are many different polymers that cannot be melted together. Sorting is expensive, the recycled material is lower quality than virgin, and virgin plastic is cheap.
The recycling symbol with a number identifies the polymer type. It does not indicate that the item is recycled in practice, and for most numbers it is not.
What contamination does
Food residue, wrong materials, and items too small to sort can cause a whole batch to be rejected. Rinsing containers and leaving out what you are unsure about helps more than adding hopefully.
The uncomfortable part
Recycling rates for plastics have remained low for decades despite public participation. The material was never designed to be recovered and the economics do not support it.
What has more effect
Using less, and choosing materials that recycle well. A drink in aluminium has a genuine second life. The same drink in plastic mostly does not.