MacBook Pro transfer to new

You'll want to make sure the late 2020 MacBook Pro is purchased from a reputable source and the new Mac is prepared properly for resale. Essentially, the procedure listed in this Apple Support article needs to be completed: What to do before you sell, give away, trade in, or recycle your Mac - Apple Support

If this new Mac isn't prepared properly, it could result in making the transition to it much more difficult than it needs to be, or in some cases impossible.

For example, all of the MacBook Pros available from Apple's Certified Refurbished store are all prepared properly, and will start up just as a brand new Mac would. For sure, I would steer clear of used Macs available on Ebay, FB Marketplace, Craig's List, etc.

Regarding the transfer from your 2013 MBP to the 2020 MBP, I can offer the following advice:

• The easiest means of transferring everything is via the use of your Time Machine backup external drive and Migration Assistant. You'd simply make sure your 2013 Mac is updated, then run a Time Machine backup on it. Once the backup is complete, you'd eject the drive and connect it to your new Mac. Migration Assistant will ask how you want to migrate, and you'd choose from Time Machine backup. You may need an adapter for your external drive to connect it to your new Mac, such as a USB A to USB C adapter.
  • I would not recommend migrating via WiFi, although it is an option. If your WiFi signal isn't rock solid, this can lead to data corruption.
• This Apple Support article describes how to use Migration Assistant: Transfer to a new Mac with Migration Assistant - Apple Support
• You may need to update some apps after the transfer, as many have versions coded for Apple Silicon Macs. You can check your old Mac to see which apps may need to be updated by going to the Apple Menu-->About This Mac--->System Report. In the System Report screen, look in the left column and scroll down to Applications and click it. The resulting window will show details about each application. If you scroll to the right a bit you'll see a column labeled Kind. There you'll want to see which ones are either Universal or Apple Silicon. Those will be fine. If they're listed as Intel, they may work fine, but will need to run under Rosetta, which would be installed the first time you need it.
• All of your settings and email account will transfer, and you shouldn't need to worry about those. Documents, photos and other data will transfer as well.

When you set up your new Mac, please write down the password you've established for it during setup. You have no idea how many forget to write the password down, and can't unlock their Mac later on. It should be noted here that your password can be the same one you used on your old Mac, so don't be afraid to do that if it's easier for you to remember.

I hope this helps.