They don't make them to be taken apart and rebuilt anymore. So a lot of that will be all on you and your ability to figure it out and do what's needed. Perhaps something has gotten in there and jammed the return spring or that little arm itself. So maybe jiggling it while blowing compressed air at that area might free it up. If the spring is broken, then it's probably a spring that won't easily be found anywhere for sale.
You might see if anyone has made a youTube video about it. I don't know how much more you'll be able to see if you remove rubber hood covers and the shift levers. But if you don't do anything you will have to buy another STI. So depending on what you feel comfortable putting back together, then disassemble to your desire. At the worst, you'll just have to buy another STI.
https://si.shimano.com/en/pdfs/ev/ST...-5800-3711.pdf
https://si.shimano.com/en/manual/sea..._model=st-5800