What is the shortest lap time ever in a Formula 1 race and where was it? Is it around the shortest track, or does the amount of turning required to get around a shorter track slow the cars down?

Valtteri Bottas with a time of 1:02.939 in the Austrian GP on 4th July 2020 (during qualifying).
https://motorsporttickets.com/blog/lap-records-in-formula-1-list-fastest-lap-times-at-every-circuit/

It's not the shortest circuit. Monaco is the shortest, but has 19 turns:

Circuit de Monaco is the shortest track on the current Formula 1 calendar, at 3.337km. Such is the short length of the track, it is the only race on the calendar which does not cover the 305km distance stipulated in the regulations. Races in Monaco instead run to just 260km.

Perhaps the most famous of all races on the F1 calendar, plenty of challenges are packed into a lap of the 19-turn track, which passes by the iconic Casino Square, through the tunnel and around the famous Rascasse cafe.

https://www.lightsoutblog.com/longest-and-shortest-f1-circuits

I suspect I have found the shortest. It was Valerie Bottas on his 3rd qualifying lap in a 2020 Grand Prix, but not the Austrian one. Due to Covid, that one was odd as it was run on the same course a week later and called the Styrian Grand Prix. It was also the first F1 race run behind locked doors.

The shortest lap took place at the 2020 Sakhir Grand Prix in Bahrain and was the first, and as at 2025 only, F1 race in this track. In this one Bottas qualified in an impressive 0:53.77 seconds. This was on a modified course from the Bahrain GP run a week earlier, but at 3.543km (2.202 miles), it was still slightly longer than the Monaco track at 3.337km (2.074 miles).

https://en.m.wikipedia.org/wiki/2020_Sakhir_Grand_Prix