RS Itinerary in Barcelona-what it does not cover...

Not sure if they are included i a walk or tour, but there are a couple other buildings designed by Gaudi that are worth a look, spending some time, maybe lunch at Boqueria Market is fun, there is also a nice Maritime/Naval museum as well.

I'd add these 'must-sees' to your list:
Palau de la Música Catalana
Museu Nacional d’Art de Catalunya
Santa Maria del Mar church
Gràcia neighborhood
Hospital de Sant Pau
El Born neighborhood + Santa Caterina Market
Museum of the History of Barcelona (Plaça del Rei)

I can’t comment on this particular tour, but looking at the itinerary it’s a great idea to spend a few days ahead of the tour. We spent 4 nights in Barcelona and covered a similar itinerary. I would also recommend Gaudi’s Casa Mila and Casa Batiló if not on your guided tour. We enjoyed La Boqueria Market for lunch and were entertained by a musician outside. Santa Caterina is another market to visit. Enjoy the amazing view and explore the different meals on the top floor of El Corte Ingles department store! Lovely. One of our favorite highlights was touring Palau de la Música Catalana. The acoustics are superb! Absolutely breathtaking both indoors as well as the facade. We scheduled this following La Familia Sagrada tour. Other favorite sites: Miró Museum, Parc de Montjuïc & magic fountain. The list goes on…
https://www.barcelona-tourist-guide.com/en/music/palau-de-la-musica.html

If your pre-tour time includes a Sunday, I highly recommend going to the cathedral at mid-day to watch the sardana dancing.

https://www.barcelona-tourist-guide.com/en/cultural/dancing/catalan-dancing-sardana.html

It was at 11:00 am when we were there in May 2019, but that may have changed. Online information says they also dance there on Saturday evening.

Make sure you book the Picasso museum in advance—-the lines are long.

Re the Picasso Museum, if you are primarily interested in seeing work done late in his life, try to find out in advance what is actually in the museum at the time of your visit. We were disappointed that nearly all of his most recognizable works we had expected would be there were out on loan around the world. We thought the music palace was wonderful, but book in advance, especially if you need an English tour.

We joined the Spain RS tour a few years ago and at that time, the Picasso Museum was closed on Monday and the lines were long on Sunday

When we were in Barcelona (about 8 years ago) the Picasso museum wasn't at all crowded. We loved it, primarily because it didn't have his more well-known works. We hadn't realized the range of his output. Wonderful representational stuff, for example.

I also recommend the chocolate museum.

And definitely catch the sardana in front of the cathedral. We were fortunate enough to be there on a religious holiday, and there was a wonderful festival by the cathedral that included gigantes, giant puppets, and the human towers castells. What an amaing evening!

I much preferred Saint Pau and and Palace of Catalan Music, both the work of Montaner, to the more popular Gaudi attractions. Saint Pau is an easy walk from Sagrada Familia.

Have a great trip!

https://www.santpaubarcelona.org/en/visits

https://www.palaumusica.cat/en

Monserrat on a day trip.

Two full days would allow you to fill in a lot of gaps, but don't count your arrival day; you're likely to be too jetlagged and sleep-deprived to accomplish much. Another thing: A lot of sights in Barcelona often (I'm tempted to say always) have very long ticket lines, and the tickets for the day may sell out long before the day is over. This makes it difficult to be a really efficient tourist, because you have to guess how long you'll need at each sight in order to select an entry time for the following sight. Tickets to a lot of the Gaudi sights, in particular, are quite expensive. I wouldn't want to pay those prices and have to leave before I had seen all I wanted to see.

Finally, the crowded conditions are not conducive to getting in and out of sights quickly. (Heaven help you if you are serious about photography.) Casa Mila and Casa Batllo (maybe also others) meter people in and out to avoid extreme overcrowding, so--unless the COVID situation has changed things--you cannot assume you will get inside the door at 11:30 AM just because you have an 11:30 ticket. Take full advantage of every morning you're in the city, scheduling one of the difficult sights at opening time so you'll be able to get in on schedule and will walk into a less-crowded building.

I'm a big fan of modernista architecture and have spend a lot of time tracking down wonderful buildings, not only in Barcelona. I actually don't think going inside Casa Vicens is a great use of your time with only a few days in the city. You may be able to glimpse the outside of it, and it's nice to spend time walking around a non-touristy neighborhood rather than just running from one indoor sight to the next. I just don't think it's worth the money and time to go inside Casa Vicens for the typical visitor.

These are the Barcelona sights where buying tickets in advance was essential even back in 2015. I suspect some of them may be still operating with some capacity controls due to COVID, which could make getting tickets even more of a challenge.

• Parc Guell: Tickets are not even sold at the sight; you must buy in advance)
• Picasso Museum: At the time of my visit the museum looked like those cocktail-party-in-NYC crowd scenes you see in old movies; some others have had a much more sane experience there, but the ticket line can be very long.
• Casa Batllo: Also totally packed at the time of my visit; it's not a government-run sight, and they are really raking in the cash.
• Casa Mila : Also very crowded, but it wasn't quite as bad as Casa Batllo; don't know whether that was a fluke of my timing.
• Palau de la Musica Catalana: As already mentioned, the English-language tours can sell out.

I had no issue getting walk-up tickets at MNAC (wonderful museum with interesting modernism collection and fabulous medieval frescoes from churches in the Pyrenees) and the Miro Museum. That's not to say you couldn't possibly run into a 10-minute line or something like that. And I don't know whether they have reduced the number of tickets being sold due to the pandemic.

As recently as 2019 I was able to walk right up to the ticket counter at the Sant Pau modernista site and enter immediately. It's great to have a sightseeing option in Barcelona that doesn't have to be pre-scheduled. It's a multi-building complex with nice grounds. Try for a good-weather opportunity if you decide to go.

I like all of Carlos's recommendations. I took the excellent rooftop tour at Santa Maria del Mar.