How long does opt approval take?

It depends when you are applying for OPT.
One of my friends applied in the first week of May he got on August 28, total time almost 120 days. I applied on June 3rd, received my EAD card on August 30, almost 85 days. If possible try to avoid the rush hour from March to May.
The following are good resources to track your application. Use the OPT Tracker on the Link on the top.

Have you tried tracking platforms like OPT tracker and reviewed response for OPT waiting time?

The most important aspect to move from F1 to OPT when you apply for OPT the earliest possible is 90 days prior to completion of your educational program.

Actually the applications are processed in the order they are received that first in first out if your application file is perfect you might reduce your opt waiting time. Generally, people say you get it earliest within 60 days’ time but a lot of them take up to 120 days.