Are Unions controlled by organized crime? Does that hamper their ability to affect politics in the US?

Then you agree that the answer to your question is “no”. You’ve learned that and more because many people were polite enough to give a reason supporting that answer.

In fact, you were given that answer in the other thread.

@Acsenray also thoughtfully expanded on that post here in post #6, whose completeness made the rest of the thread redundant.

As for the lobbying aspects, OpenSecrets reports that total federal lobbying ran about $3.8 billion in 2021. Of that $66 million was from the U.S. Chamber of Commerce. No question that’s a significant sum of money, but it’s less that 2% of the total. You need to look at the overall split in lobbying between business and other groups. Business is a proton to labor’s electron. Why? They have all the money. The mob at its very biggest in history controlled less money than any individual major bank or corporation. Their power has always been muscle. The muscle economy is long gone.