are they fair game or are the foragers thieves who are committing a crime?
The former. You placed the items in a trash can, which clearly indicates an intent to abandon ownership, and put them on public property. That said, according to one California city's website (not Los Angeles), this sort of scavenging violates the California Public Resources Code. The website did not identify the particular section of the code, so I'll leave it to you to peruse if you like. Even if that's true, as you acknowledged, the LAPD isn't going to do anything about this.
No so fast. The OP mentioned "bins" and "recycling." That makes it illegal in Los Angeles County. Additionally, many, if not most municipalities within the county have similar ordinances.
https://pw.lacounty.gov/general/faq/index.cfm?203=203&Action=getAnswers&FaqID=IyM9PzcK&Keywords=1
I haven't looked at this in a while, but my recollection is that the Los Angeles County ordinances generally only apply in unincorporated areas in the county and would not apply to the OP who is in the City of Los Angeles.
I worry that these scavengers might find some doc, like a credit card bill or bank statement, and run with it
If you're discarding documents containing sensitive personal information without shredding them, you're being foolish.
IS throwing trash into somebody's semi-empty can in the street illegal
No.