I don’t know about the process, but 0.8% for 6 years is a pretty good deal I would say.
You would probably get closer to 1% right now for the same duration, and SARON margin around 0.7%.
So unless you really want a longer fixed-term mortgage like 10y (which will come at a significantly higher rate), I would take it. SARON isn’t going to be much better than that given the generally increased margins nowadays, but with significantly more interest rates risk.
See Mortgage rates in Switzerland [2025 edition] for discussions about current rates.