I am thinking of adding a "Send Feedback" button to the bottom right corner of my SaaS (web site). Is there any good service for this? (For example, a service that allows me to do this by simply putting a script tag in my HTML... And a free trial would be even better)

What should happen when someone clicks the button? Are you thinking of something like at the bottom right of this web page? https://boxyhq.com

I need some kind of survey. Users can report bugs or send nps(Net Promoter Score).

Have you looked at Mautic? https://www.mautic.org/