Here are the methods I know to find transparent, standalone portraits of Blue Archive characters in PNG or Spine2D animation format. If you know of any others, feel free to leave a comment.
The repository i use is blue-archive-spine-production. This repo's data updates when the Google Play version of BA updates (Global, once every 3 months; JP, once every month). If you only want a few characters and a small selection of NPCs, there are 2 outdated repos that haven't been updated for over a year: Schale-Archive and blue-archive-spine. You can use download-directory.github.io to download the entire spine folder or individual character folders.
Kivo.wiki is a Blue Archive wiki in Chinese. Under each character is a function called Appreciation Mode (鉴赏模式).
Here you can view a character's Spine2D animations and download them as very large images, over 1000x3000 pixels. The path for these assets looks like this:
https://api.kivo.wiki/assets/spines/[sprite name]/[sprite name].png
https://api.kivo.wiki/assets/spines/[sprite name]/[sprite name].skel
https://api.kivo.wiki/assets/spines/[sprite name]/[sprite name].atlas
For example, Yuuka's would be https://api.kivo.wiki/assets/spines/yuuka_spr/yuuka_spr.png
You can replace the [sprite name] portion with a character's filename. Here are 2 indexes that list them all.
Google Drive - https://drive.google.com/drive/folders/1SRgjsqei_pgkCEp8x6DI7iRgqKn1rN-x
My gist - https://gist.github.com/pkpc9/5786820b588cf026757d44e57c991e4f
Blue Utils is a Blue Archive wiki in Korean. On any character's page, press the "Show full illust (Spine2D)" button. It will show a standalone PNG of that character, followed by a link to "Show All Character's Spine2D (Google Drive)". This links to a Drive folder called BASpineExport, which contains PNG files of every character and their individual expressions.
Options 2 and 3 are constantly updating, so I recommend them if you want new characters quickly.