Timing Logistics For Parc Guell and Sagrada Familia

I would recommend a minimum of 2 hours-3 is better-for Park Guell as there are nice paths to explore and some houses from when it was going to be a planned community.
As for transportation back to Sagrada Familia, I would choose to walk. It’s a 30 minute straightforward walk along pleasant streets. The underground is possible but doesn’t save a lot of time. Since Barcelona is so walkable, we didn’t use taxis, etc., so can’t offer advice there.
Please allow plenty of time for Sagrada Familia. The interior astounded us so we spent lots of time gawking and admiring the amazing light. We were there at least 3 hours which might be longer than most, but it was worth it.

You don't have a lot of time to see both sights. I would plan on spending one hour maximum on Park Guell, and then taking a taxi back to Sagrada Familia--about 30 minutes between these sights. Don't walk--you don't have enough time. Taxis are best.

A couple years ago, pre-COVID, we did both Parc Guell and Sagrada Familia in one day.
We did Parc Guell in the AM, because it was cooler in the morning. What month are you going?
We had guided tour tickets at 10:00 for the Monumental area. The guided tour is only an hour or so, and then spent 1 ½ hour on our own visiting the the monumental area, then the park outside the monumental area.
We walked down to the metro station, but you can take a taxi to Sagrada Familia to save time.
We had 2:15 pm guided tour tickets to Sagrada Familia. We had ample time to wait at Sagrada Familia before being allowed to enter.
With those two timed tickets, we did not have to rush or feel rushed. We had ample time to see both places.

Thank you for sharing your experience. We will be there in July. Hoping to do Parc Guell in the morning with time for lunch before Sagrada in the afternoon