Can anyone recommend a service that will unsubscribe from now unwelcome sites?

The irritating thing was that nobody would admit it, or describe it, or tell me how to get it to happen.

My credit card expired, and all payments continued happening peacefully on the new card. Then the other card expired and no, that never happened, we never continue payments when we give you a new card,

That was a long time ago, and all my suppliers now contact me when a card is about to expire.

So it doesn’t work for me, but it wouldn’t surprise me at all if it works for you, because the Banks and Credit Card companies were never so organised that their staff actually knew what was going on.

What makes you think you need a shady scam company to get rid of another shady scam company? Do not do it!

Turns out scam victims are a rich seam of income for scammers - I make videos about scams for YouTube and I am constantly dealing with spam comments (from other scammers) claiming that they are victims who hired a hacker, and that hacker recovered their money for them.
In my scambaiting mailboxes, one of the more common scams is the ‘scam victims compensation award’ scam - where the scammers claim they represent the government of some West African country and want to make amends for a previous scam - that is, these scammers are targeting people who have already been scammed once.

Does not surprise me at all, I guess having been scammed once actually increases the probability that you will fall for their trick again. Scammers know what kind of people they are looking for and the relevant personality traits (I am guessing: trustfulness, naïveté, being “not a real sophisticated computer user” in the words of the OP, etc.) do not change with experience.

This. Some scammers purposely use misspellings, make outrageous claims, use symbols instead of letters in the subject, click here to unsubscribe link, etc. to lure in the gullible. If you see all these signs and still respond or the the email, you’re a likely candidate for the scam and it continues from there.