Was it a big mistake to buy an airline ticket from Skyscanner

I don't think it was a mistake at all. Despite what others have said here on the forum, I've never had a problem with Skyscanner, Orbitz or Kayak. I have used all three of these 3rd party booking sites and it has always been fine.

It will probably be fine. You will want to look up your British Airways passenger record locator to make sure the reservation was actually ticketed. The only other issue that can come up is if a problem develops either for your flight or for your situation which requires a change of some sort, you will need to deal with sky scanner who will then deal with the airline. It just adds another layer.

Don’t spend too much time worrying about this.

I've used Skyscanner in the past and it's been fine.

People warn against booking through such sites, because it's easier to deal with a problem, if one arises, if you've booked directly with the airline. But that doesn't mean that the site is bad or a scam.

Thank you everyone. I feel a lot better!

You're also only talking about Rome to London, so there is little that can go wrong. It isn't like a transatlantic flight for many hours in a cramped cabin where you may need to change something.

There are lots of flights on that route by several operators.

Many who booked via an OTA (Online Travel Agency) at the beginning of the pandemic failed to get refunds or credits as the companies and the airlines played the blame game. This particular complaint has been largely solved, at least in Europe, since the airlines have agreed to refund customers who have booked through OTAs in future. https://thepointsguy.com/news/european-canceled-flights-passenger-refunds/
The reason to go direct to the airline is that booking through an OTA gains you exactly nothing yet you are further removed from the provider.

booking through an OTA gains you exactly nothing

No, not exactly the price of a flight or hotel was always cheaper in all the cases I have used them over 20 years experience after checking the price of booking directly.

"booking through an OTA gains you exactly nothing"

I have rarely booked directly though an airlines. OTAs provide more competition and lower prices. I have compared American and CheapOair side by side when booking and have saved hundreds of dollars when going with the OTA.

I’ll just reiterate that when booking through a third party site and something does go wrong, e.g., flight cancellation, you deal with the third party who then deals with the airline. I’ve only booked once through a 3rd party site, flight was cancelled. I had paid extra to go through a specific airport rather than another that would have added a couple hours to the trip due to a longer layover. When cancelled, I still went through the airport I didn’t want to go through and never got a refund of the extra I paid for a preferred airport. Now, I always book directly through the airline.

There have been many, many complaints about CheapoAir, most definitely pre-dating the pandemic. I would never, ever use that company. I don't really doubt that some of the third-parties out there are basically honest; with them, it's a question of whether you're saving enough money to justify the risk of extra hoop-jumping if your flight is cancelled or rescheduled. With companies like CheapoAir, any such change in your flight schedule is looked upon as an opportunity to rip you off.

Thank you everyone. I went ahead and called American Express and requested a block to the charge and then went ahead and booked directly with the airline. Even that was a little suspect as I thought I was booking through British Airways and then when I noticed an error with the name, I called them and found out the flight was actually a Vueling flight. I was able to correct the error but not able to get a seat assignment. I was told I had to go online a week before the flight to request a seat assignment.

A friend of mine has a heavy foot when he drives. He likes to drive way over the speed limit. He knows others who like to do this. They all bragged that they didn't have to follow the speed limit on a certain route because no one every got a ticket.

Until they did.

Buying from a third party site can save money. If everything goes right, you've done well. If things go wrong......??????

I prefer to buy direct. It shows loyalty to the customer service rep over someone who hasn't. I also join every airlines frequent flyer program and make sure my number is on the reservation. It costs nothing but tells them I am part of their frequent flyer program. Even with low status, I'm one leg up on those that are in the same class as I am but not a member.

Vueling and BA are both parts of the same family, under the same umbrella

I used third party sites many, many times in the past and had no problems. I switched to booking direct with the airlines after others on this forum suggested it was the better way to go. You’ll probably be fine.

Thank you everyone. To play it safe, from here on out, I will book directly with airline.