Thoughts on my Barcelona plans?

Pace seems right, would help to know time of year for your visit.
For me Parc Guell has lost its charm since being fenced off and creating a cow herd mentality. Tickets are expensive and folks tend to linger in order to "get their monies worth" while clogging the vistas.

Thank you, will be there in late June.

A few initial thoughts:

A "tapas lunch" does not exist, we locals go out for tapas in the late afternoon or early evening as a pre-dinner snack. I would be weary of an establishment that offers "tapas" for lunch as potentially a tourist trap, same goes for places serving paella for dinner. Know that the mealtimes in Spain may be different than what you are used to, for example lunch service starts around 2 pm and dinner service starts around 9 pm.

I agree that Parc Güell has become overrated these days, since you are in the area I highly recommend at least visiting the nearby Hospital de Sant Pau, a turn of the century hospital built in the modernist style, now a UNESCO World Heritage Site opened to visitors, very nice to explore with a fraction of the crowds as Parc Güell.

If you are looking for a neighborhood to explore with authentic charm, I suggest visiting the Gracia district specifically the Vila de Gracia area, one of the last corners of Barcelona still with local life. It is the "hip" place to be now, with its co-working spaces and artist studios, but also feels very cozy and welcoming. You see many young families living there, kids playing futbol in the neighborhood's various small squares, it has a small town feel. Gracia is within walking distance to most of the Gaudí sites and has good access to public transportation.

Ah......beware of the heated swarm of fellow tourists. Seriously, stay hydrated to avoid baking your meat in the heat. A great benefit of summer is the additional hours of daylight so strongly advocate immediate adjustment to staying up late. Evening walks are wonderful and a great way to assimilate into the local culture. When dusk falls the locals come out, seek wide blvd to watch the families engage and then find a local place to eat.
In lieu of Parc Guell recommend visiting Gaudi's first home, Casa Vicens. Far more intimate of an experience plus a good walk back to Plaza Cataluna offering a variety of architecture, local shopping and dining experiences. You will find few tourists in these environs.
Add this gem to your time after visiting Sagrada, Recinte Modernista de Sant Pau.
A nice walk north of Sagrada offering an architectural experience few take the time to visit.

Although I agree that Casa Vicens most likely will be pleasantly uncrowded, as a fan of modernista architecture, I was disappointed by the interior in comparison to the other Gaudi sites I had visited (which is most of them). Sant Pau, on the other hand, is large and beautiful, as well as under-visited.

Your itinerary seems over-scheduled, especially with the heat and crowds. Others above have mentioned some good alternatives. Regarding meals, our local guides told us, “If you go to [an eating establishment] before 13:30 or 19:30, you will not get freshly-made dishes. Avoid eateries with photos of the food out front.

Barcelona is very interesting for tourists. Therefore, you can just fly there and walk around for days, admiring the architecture, which is simply magical, and take a lot of photos

My two cents:

You didn't mention when are you visiting... and while Barcelona is visited by tourists all year round, it really makes a difference whether you're in town say in July or say in October. This is to say that whether you may be overdoing it or not it's also related to the time of the year you're visiting.

Having said this, and assuming you're visiting anytime from May to October...

• keep in mind the heat, which due to the humidity on certain days during these months can be considerable and really punches you, depleting your energy quite quickly I must say.
• for day 2 I have a suggestion: https://community.ricksteves.com/travel-forum/spain/infox-in-bcn-visiting-the-sagrada-familia-and-then-park-guell-or-the-other-way-around
• day 5 seems a bit tight, I would drop one of the three, or maybe visit the third one in the evening (ie Casa Batlló)

On a different note: on your first days you mention "the major neighbourhoods", which would those be? The 'major' neighbourhoods, from Sarrià-Sant Gervasi to Nou Barris, among others, are not frequented by that many tourists.

Ah, and it seemed appropriate to me to revamp this old post of mine here, in case it can be of interest: https://community.ricksteves.com/travel-forum/spain/barcelona-palau-guell-or-park-guell

Enjoy!