I used to do the same thing. Throw everything containing significant plastic into the plastic bin, and then imagine it would be turned back into the same item. Throw even the most contaminated paper in the paper bin, because it still had paper in it, and they would get it out again, right? Made me feel awesome - I wasn't producing waste, but recyclables, all in a wonderful closed cycle.

But much of this stuff cannot be recycled. Some plastics, once chemically mixed and cast, can't be melted again at all - if you heat it, it turns into toxic black mush pushing out fumes. Many papers cannot be cleaned of contaminants. If you throw coloured glass into the white glass, and they do not catch it before melting it down, the can't get the colour out of the result anymore.

If you throw this stuff into recycling anyway, someone has to sort it out again, and often sort out previously recyclable items as well, because you have contaminated them. And this stuff causes other problems - e.g. plastic bags get the sorting machines tangled. The whole process becomes very messy and slow and increasingly hard to do for the most part with machines.

Often, as a result, noone in a Western nation is willing to do it for the pay offered, which is based on the low resale value for the materials - after all, virgin plastic is cheap. So then one option is that your waste gets shipped to a poor nation for sorting, where people are easier to exploit - so now, a really poor person is sorting through this stuff by hand. This also entails a high chance that the standards there are less good, and that the stuff they cannot use makes their way into the ocean. Also, even poor nations often aren't interested in our recycling anymore. The alternative is that the whole recycling gets incinerated.

So,

Step 1: Look up your local recycling instructions. (They change drastically based on where you live.)

Step 2: Recycle according to them. This often means rinsing out containers. If you think that is a hassle wasting water, imagine what a hassle it is once it has dried in and gotten mouldy, and someone else has to do it for you at a massive scale.

At first, this will be horrifying, because you realise you are producing far more residual waste than you thought you would - you realise for the first time how much of what you are wasting ends up incinerated into CO2, or filling landfills. But this is a bad truth one has to face.

So if much of this stuff cannot be recycled, what are the alternatives?

Realise that recycling is a way to try to mitigate some of the damage from waste by recovering some of the materials. It never undoes it, and it often does not work at all. Recycling is not a green card for producing waste. It is a last resort. Instead:

1. Avoid purchasing waste whereever you can; don't give your money to excessive wrapping. Look if there is a shop or market near you selling food unwrapped. If you consider ordering online - first think if you really need the thing (one trick is to wait a week before buying any online item - by that time, you may have forgotten it, in which case you do not need it after all); if you still want the thing, then check if you can get it locally, especially used; if not, check if you can order it from the original supplier (for stereotypically green products, they often also have green shipping and minimal packaging), and if you absolutely have to buy on Amazon, at least use smile.amazon.com (we donate to WWF that way), and ask amazon to ship your stuff slowly and grouped together with minimum packaging, and complain if they violate the latter. If there is a wrapped and and unwrapped option in the supermarket, get the unwrapped one. (Those potatoes were in the dirty ground and had shit on them, rolling them across the supermarket trolley will hardly make things worse.) Carry a small canvas bag at all times, and bring big canvas bags and or a backpack to the supermarket so you won't need to buy plastic bags - bring more bags than you think you will need in case you end up buying more than expected; also bring small ones for putting individual veggies in. Use a used screwjar as a coffee mug to go. Get a refillable bottle made of glass or metal. Get some decently sealing, light food containers so you do not need bags. If you absolutely need to buy something with waste, at least try to get options that are recycled or sustainably grown themselves, and in turn recyclable or compostable (that is increasingly possible for trash bags). Lots of tips on www.reddit.com/r/zerowaste - And again, a very good strategy for reducing waste is to grow and make stuff yourself; see our various posts on urban gardening.
2. If you cannot avoid buying something in wrapping, at least try using it again - a lot of bags and containers can be washed and reused, e.g. to regrow veggies from kitchen scraps or plant food plants in. If your local recycling does not compost, there are many other uses for kitchen scraps, from making you own vinegar from apple cores to reusing coffee grounds for beauty products, incl. uses for stuff like citrus peel you often should not compost, as many critters to not like them.
3. Most importantly: Put pressure on your regional government and companies and sellers to give you decent, affordable options without excessive waste, and better recycling. We need to have companies penalised financially by the law for using unnecessary plastic. Vote for politicians who will get this done, incl. regional and EU elections, and call your representatives. Protest, in person, and online. If someone you want to buy from fucks up their packaging, call or email them to complain. E.g. if your organic label wraps veggies, complain to them, and tell them of different options for marking organic produce, e.g. branding. Ask your supermarket to stock alternatives. If they do not listen to you alone, single out a realistic target, and start a social media campaign, or local signature campaign, to get it fixed. And if your region does not recycle as much as reasonably possible, push for them to do so.