While SARP's FTL is very fast, the STL speeds do slow things down a bit. Let's check the
Starship Speed Standard page.
Assuming that most transits aren't using cutting-edge military tech (due to lack of availability, lower maintenance needs, pricing, etc) we have ~45k km/s for a standard ship, ~60k km/s for an advanced ship, and ~75k km/s for a very advanced ship for 'average' speeds. I imagine a lot of the transits would be in the 'slow' category, but we'll use average for now.
For the first speed, it would take about a day and a half to travel the distance from our Sun to Pluto. If reddit's math on the sun's hill sphere is correct, it'd take 2700 days to reach the edge of the Sun's hill sphere. Somewhere between there is where FTL travel is possible, because you can't FTL within a (strong enough) hill sphere. Let's assume it takes ~4 days on average.
So while FTL travel to anywhere takes 2-3 days, you need to add on another 3-4 days of transit per system to load your goods, drop off your goods, etc. I like this, personally, because it does create opportunity for pirates, patrol routes, etc, etc.
As for how well supplied and/or self-sufficient each planet is, I'd say it depends. Most crucial food, water, etc, is likely sourced locally or from somewhere within the system. I think this is more of a supply chain thing than anything else; if you can shave off 6-7 days from a delivery schedule for an entire planet, it's probably worth the investment.
Less crucial goods, such as specialty clothes, imported spices, jewelry, technology, etc, would take the full 7-11 days of transport per trip. Multiple freighters are probably used to reduce this window down to something reasonable - anywhere from a delivery once per day, once per hour, or more - but an interruption to the supply chain would likely be felt in a matter of days as luxury/supplemental goods become unavailable. I don't think a planet would be crippled by something like a blockade, but the quality of life would probably drop off quickly.