We will be in Barcelona from February 18-22. We are looking at the Barcelona Card.... skip the lines at all sights and unlimited transportation. What are pros and cons of no pass vs pass. Who has experience with and without.
Note the exact wording on the Barcelona Card website [emphasis mine]: "it can also help you skip the queues entirely at many of Barcelona´s most popular sights..."
I have taken a quick look at the Barcelona Card website, and I don't see a list of the covered attractions. I assume it's there somewhere. From poking around, though, I suspect that a lot of the key sights are not covered by the card, because I see that you can buy those tickets separately. That includes La Sagrada Familia. So I am unable to tell whether the card offers a good value for any tourist, much less for you in particular.
The decision about purchasing a city card comes down to the individual tourist. Barcelona has at least six very popular sights for which you'll need a way to avoid the ticket line. Many if not all of them sell timed tickets. Be sure the card doesn't leave you standing in a long line waiting to acquire a timed ticket. It doesn't matter if you get that ticket for free if you've been standing in line for over an hour. (And you might get to the ticket booth and find that there are no tickets available until the next day.)
There's a bit more detailed information here. The only one of the six biggest-problem (longest-line) sights for which the card gives you skip-the-line privileges is the Picasso Museum. For any of the other Big 6, planning to use the card for entry effectively keeps you from simply buying an online ticket in advance so that you avoid the ticket line altogether.
It appears that the card also covers Casa Mila and Casa Batllo--though I'm not positive they are fully covered as opposed to simply discounted. You'll be buying your own tickets (if you want to see them) to La Sagrada Familia, Parc Guell and the Palau de la Musica Catalana.
Do not over-value the city-transit benefit. It is very easy to buy a T10 ticket that gives you ten rides on the buses and subways for something in the range of 1 euro per ride. The ticket can be shared by multiple travelers; just swipe it once per traveler.
I urge you to carefully read https://community.ricksteves.com/travel-forum/spain/need-recommendation-to-get-city-pass-or-another-type-of-pass since some of your premises above are incorrect.
Note as well you're looking at a resellers' website, not the official website of the card, which is https://bcnshop.barcelonaturisme.com/shopv3/en/product/1/barcelona-card.html?o=h
(Btw I just saw Ann has also mentioned the official site)