I don't know which tour you're on, so I don't know which sights the tour covers.
Having just glanced at the website, I'm very doubtful about that card. Americans who don't commonly use public transportation at home tend to over-value the transportation benefits on cards like that. The fact is, it's very easy to buy single tickets or day passes for public transportation in virtually every major European city. You don't need to buy a multi-day pass which is probably priced on the assumption that's you'll use the buses/Metro a lot--and you may not. Barcelona is a very walkable city with very attractive architecture. Just wandering around on foot is a great way to see it.
As for the rest of the card's benefits: The sightseeing discounts highlighted on the website are all 15%, which is a laughably small discount, hardly worth even thinking about. Then there's this: "...You can also enter for free to some attractions with the card. We have not listed which ones here because the offers change frequently. You will be informed which ones when you are presented with the card." You've got to be kidding me; talk about buying a pig in a poke. Elsewhere on the website it says Casa Batllo and Casa Mila/La Pedrera are discounted (probably by that paltry 15%, I'm guessing) and that the Picasso Museum is free. The Picasso Museum is worthwhile (but some of Rick's tours cover it). But is the bit about free entry to that museum even accurate at this point? Why isn't it on the main web page, if so?
As for the reference to skip-the-line tickets, the places where that is needed will in many cases either be on your tour (La Sagrada Familia and perhaps Parc Guell) and/or are just discounted (Batllo and Mila). It's very easy to buy tickets on the web sites of the individual attractions. Those will be time-specific tickets that keep you out of the long, ticket-buying line. In the past, there was sometimes a 10% discount for buying tickets online in advance at some sights; I haven't checked to see whether that's still the case.
This looks like an overpriced transportation card with some minor additional benefits added to make it look like more than it is. It's the silliest-looking basket of benefits I've ever seen. Perhaps COVID has complicated the process of getting sights to sign up.