Barcelona crowds?

One of the most touristed cities in Europe is bound to be very crowded "in normal travel times". But "normal" doesn't apply anymore, so I'm not sure you can use it as an effective comparison point. The future is yet to be written.

Another, very crowded, response. Not terrible certain times of the year, but always busy. Keep a close eye on your belongings as there are plenty of pickpockets out and about, just like in any tourist destination.

In normal travel times, just how crowded can I expect Barcelona to be?

Depending on the week of the year, ranging from busy but all right to very busy. Note that it's not only tourists but also congresses, sports and music events, etc. that bring nearly 18 million visitors each year to a city with a population of 1.9 million (4.5 in the metropolitan area).

I must insist in that it's depending "on the week", not the season, and it'll depend on both the local events (festivities, holidays, etc) as well as events hosted in the city (business, competitions, concerts. etc.) that are happening that week.

Some food for thought: mass tourism has been visiting this city for over 70 years now, and since the last 30, figures have exponentially increased, so it's unlikely it will change (too much) any time soon.

Depends on time of year. I went in late May and it was wonderful.

From reading posts on this forum pre-pandemic, it seemed pretty clear that tourism was continuing to increase. The importance of advance-booking tickets at the most popular sights became more obvious year after year, based on comments here. Even back in 2015 quite a lot of sights were selling time-specific tickets (primarily the Gaudi-related spots, the Palau de la Musica Catalana, the Picasso Museum, and the Camp Nou (soccer/football) Experience. One of the recent changes was that Gaudi-designed Parc Guell stopped selling on-site tickets completely.

Conditions inside the following places were far less than ideal even at the time of my 2015 visit (listed from worst to least bad): Picasso Museum, Casa Batllo, Casa Mila, La Sagrada Familia, Parc Guell. The (totally skippable except for logistical reasons} Ramblas was really packed and reportedly a feeding ground for pickpockets. We heard here about an uptick in crime in the Barri Gotic, which I imagine had gotten busier since my 2015 visit, but that's a part of the city I didn't get back to during my short 2019 stop, so I don't know how different it felt in 2019.

That said, I spent a lot of time just walking around the city and found most areas perfectly lovely; in my experience this is typical of tourist hotspots that are larger than small villages--visitors tend to concentrate in the immediate area of a handful of guidebook-listed sights. And the Sant Pau modernista site still welcomed walk-up visitors in 2019.