I have had calendy and didn’t have these problems in the past. Do you need a paid membership to prevent Calendly from offering appointments when there is something already scheduled (ie double booking). Also i’ve never seen the buffers show up on my calendar before. Buffers were just included in my availability slots.
I do have a calendar connected, available hours set up, and i’ve checked settings. When I click on the free busy option it just takes me to which calendar is connected. I have verified that the correct calendar is connected. My goal is to set up 20 min appointments during my available working hours with a 5 min buffer before and after which in theory would allow people to book an appointment every half hour unless I already have something that conflicts with my availability already on my calendar.