Does a cleaning crew (for cleaning clutter) have the right to take what they please?

No, they don't have that right.

Actually, I have never heard of a landlord sending out a cleaning crew for an occupied home.

It means ... likely one thing. The OP has a pretty terrible/dangerous hoarding problem. So, I can imagine that the landlord and the cleaning company were skeptical on the OP's claim to send the recyclable cans/bottles in a timely fashion.

This might be a case of the OP not making her proverbial bed and now she's got hit with the unintended consequences.

A bit presumptuous of the landlord to do this, don't you think? Unless it was a safety issue and she agreed to it. Weird story.

Not failing to mention that at 5 cents per can or bottle? She would likely have 2000 bottles and cans to make $100. A fair amount of these bottles and cans are likely beer and alcohol containers.

What are the odds, she rinsed any or most of the cans before throwing them into the shed? That shed must reek of stale beer and booze.

And I'm usually very cynical about landlords and their motives. But in this case? I suspect if hoarding is the issue? We're dealing with fire hazards and possible pests (bugs, rats, mice, etc...). I suspect the landlord hiring a cleaning crew is a sign of desperation, if not necessarily compassion towards the OP.

Most of the stuff was stuff in boxes from my previous residence like mail that I usually shred, books, clothes, etc. Enough that there was barely any walking space. I would have put it in the basement till I can go through it a little at time if the stuff didn't turn all moldy like at my previous place where all the boxes in the basement turned moldy. And yes I agreed to do the services as it's just too much to go through at once but they didn't have to go through the shed as it's not even a livable area

Was that the agreement going into the work?

By your own admittance, there was barely any walking space and the same boxes you had at your previous place and they turned moldy. You shlepped
the same moldy boxes to the new apartment? In addition you had empty cans and bottles collected that would yield $100. Not sure how much money you get per bottle, but you must have had at least 200 cans/bottles, right?
I can see why the landlord was hesitant and wanted a good cleaning and getting rid of your old boxes and masses of cans/bottles.

You fall under the hoarding category and yes, most hoarders don't admit
they have a problem. You should be happy that the landlord was nice enough to have a cleaning crew sent over instead of terminating your lease.

Pardon my nitpicking but you made a math error. If it was $100 in value that’d be 2000 bottles - not 200. That means if they were not cleaned and smell free, it would have meant it was a health and a safety problem.

Bottom line is that the OP ‘s landlord had the right to get rid of a health and safety hazard. It is his responsibility to keep his property and its storage facilities free of problems and pollution, especially when his tenant is negligent.When the OP moved in, he should have cleaned up his mess instead of sticking in storage.

Oh my, I have no idea how much money you get for returned bottles and cans,
but OP said he usually returns them once a month, so how does he get 2000 bottles together in 1 month? OP must be a hoarder

No they weren't moldy boxes I brought. I said I didn't want it to be like my previous place where the boxes there turned moldy by sticking it in the basement. This was all new boxes that I didn't want to take a chance again by sticking it in the basement. With other stuff in my life I just didn't have time to go through it soon enough

If anyone wants to know how I get alot in can redemption in 1 month a majority of people leave their cans out for me and I go through some recycling bins every recycling week and those people allow it as long as I don't make a mess. Does it matter if the cans are outside in the shed, since the purpose of a shed is to store stuff.

It depends where you live. Here in SoCal it would matter as the cans would attract lots of critters and tons of ants, regardless if they're in a shed or not.
You'd get so many ants that you'd have to call pest control.