Does the new version of Litchi allow you to download the video and photos from the SD card on your drone to your device?

Nope.  no option for that in 4.20 - might be worth requesting in the Litchi forum  - https://forum.flylitchi.com

Hello there GTS 350. Thank you for reaching out and for these information that you have posted. Since this is a 3rd party application ( Litchi ) I hope that you will get the best information from our fellow DJI co pilots who are using the said application and with regards to this matter. Just a reminder that DJI does not recommend for you to your 3rd party application like Litchi when flying your DJI Drones. These 3rd party applications might affect the said DJI drone when in use. There is a possibility that these 3rd party applications will be able work but, since it's not tested by DJI we cannot guaranteed the stability of the said 3rd party applications if it will work all the time with no issues and might void the warranty of the said DJI product. Thank you.

DJI Stephen Posted at 1-28 01:57
Hello there GTS 350. Thank you for reaching out and for these information that you have posted. Since this is a 3rd party application ( Litchi ) I hope that you will get the best information from our fellow DJI co pilots who are using the said application and with regards to this matter. Just a reminder that DJI does not recommend for you to your 3rd party application like Litchi when flying your DJI Drones. These 3rd party applications might affect the said DJI drone when in use. There is a possibility that these 3rd party applications will be able work but, since it's not tested by DJI we cannot guaranteed the stability of the said 3rd party applications if it will work all the time with no issues and might void the warranty of the said DJI product. Thank you.

If only your app had the same capability as some of the other apps available we wouldn't need to use 3rd party apps.