I found this article.
How Seville transformed itself into the cycling capital of southern Europe | Cities | The Guardian
Oh, and the "map"
Ride the City - Sevilla

It sounds like your city has made quite a bit of improvement over the past.

I think this is the SE-30 on Google.
https://www.google.com/maps/@37.3690.../data=!3m1!1e3

If you are talking about connections on the East end of that bike bridge (Puente de Hierro), then it does appear as if the connections are a bit wicked.

Adding a bridge or tunnel during original construction is probably much easier than retrofitting it on an existing road. Building, a new bridge could be very expensive, so I can imagine this being an uphill battle, but perhaps worth it in a city that is investing in bicycles.

It looks as if there are, or could be good roads/paths headed north. What is that big open area marked Charco de la Pava / Parque Vega De Triana? It would appear possible to cut a road north into the park, then connect into the city from there.