Does Adobe premier pro works smoothly in 13.3 inch APPLE 2020 Macbook Pro M1 -8 GB/256 GB SSD?

I tested a 2020 MacBook Air with only the base specs. The 13-inch MacBook Pro of that era has one additional GPU core enabled (8 cores versus 7 cores).

Although my PugetBench for Premiere Pro scores using both the legacy 0.95.6 version and the current 0.98 version were decent overall for what the MacBook is, I would very, very strongly recommend an external 2 TB USB 3.2 Gen 2x1 or better SSD. 256 GB (of which only about 150 GB would remain available after the required programs are installed) is woefully inadequate for projects, footage and exports combined (exports can run into the tens, if not hundreds, of gigabytes per file). Add to that the fact that SSDs do degrade in performance when more than about 70 percent full, and you would not even want to export intermediate video files encoded with mezzanine codecs at all onto the same internal SSD. That overly small SSD is only good for transcoding one highly compressed video file to another, with noticeable degradation in image quality from one to the next.

Now that that the M2 Pro and M2 Max 14-inch MacBook Pro are available, you should be able to find an M1 Pro or M1 Max 14-inch MacBook Pro at a good discount.

Whether you go with a 13-inch MacBook Pro or 14-inch, I'd opt for 16GB of RAM and 512GB of internal storage as the base.

The hard drive is too small and 8 GB RAM is not enough.

If you will be editing 4k, you want 32 GB RAM.