Triana area of Seville

In 2017, we stayed at the Becquer Hotel, which is a short walk from the Puente de Triana. We spent a good deal of time strolling around the Triana, and felt perfectly safe.

Everyone has their own comfort zone, and I don't wander anywhere late at night (I am not a night owl) so I had no issues wandering around Triana the Sunday afternoon I was there. I would consider it as my lodging location next time in Seville. As you intimated, it is sort of like the south bank of several large Italian or Spanish cities....narrower streets, fewer glitzy store fronts, honest local working class.
I found it great for people watching (something I only do on vacation). Families heading into restaurants to catch up between generations. Young men in tuxes, ties undone, arm in arm in the street. Smiling after post-wedding reveries, not sick and hung over. It was one of my better days in Sevilla.

I walked around the day in Triana and it was fine. As for desirability, everyone is different. I stayed at Hotel Amadeus in the Jewish Quarter/Santa Cruz and loved the neighborhood and walkability. Most parts of central Sevilla are safe for tourists.

Crossing the bridges on foot shouldn't be a problem. Many people combine walks through Triana, at least near the river, with other sightseeing on the "main" side. I think Triana would be a good choice for overnight, for the same reasons Oltrarno worked for you in Florence.

Just came back from Seville and we stayed at the Hotel Monte Triana. Completely safe area. Taxi from the airport was 32 Euros. It was less than 10 minutes walk to the Isabel II bridge and from there another 10-15 mins to most of the central attractions. How good is your Spanish? There are lots of little tapas restaurants and bars in Triana but you'll need a basic understanding of Spanish food to get the most out of the area because there is almost nothing in English. If you stay in Triana at least go to Mercado Triana where you'll find places to eat but we found it best for lunch (Fundida was our favourite). San Jacinto is the main street for cafes and bars in the area but we spent most of our time in the side streets. We used a little bar called Mondo for evening drinks. We had breakfast in a few places but agreed that a place called La Manuela suited us best. If you go to cafes/restaurants then all offer a Spanish menu and for any other languages you have to scan a QR code but the QR menu is a fraction of what is on the Spanish menu. For big places like the Cathedral and the Alcazar make sure you book your tickets in advance and they won't let you in until at least 15 mins before your ticketed entry time. Really enjoyed our trip, hope you do as well.