In ImageMagick command line, you can convert base64 files using the INLINE: mechanism. For example:
convert 'inline:data:image/gif;base64,
R0lGODlhIAAgAPIEAAAAAB6Q/76+vvXes////wAAAAAAAAAAACH5BAEAAAUALAAA
AAAgACAAAAOBWLrc/jDKCYG1NBcwegeaxHkeGD4j+Z1OWl4Yu6mAYAu1ebpwL/OE
YCDA0YWAQuJqRwsSeEyaRTUwTlxUqjUymmZpmeI3u62Mv+XWmUzBrpeit7YtB1/r
pTAefv942UcXVX9+MjNVfheGCl18i4ddjwwpPjEslFKDUWeRGj2fnw0JADs=
' b64_noseguy.gif
or to pipe the output to some other tool:
convert 'inline:data:image/gif;base64,
R0lGODlhIAAgAPIEAAAAAB6Q/76+vvXes////wAAAAAAAAAAACH5BAEAAAUALAAA
AAAgACAAAAOBWLrc/jDKCYG1NBcwegeaxHkeGD4j+Z1OWl4Yu6mAYAu1ebpwL/OE
YCDA0YWAQuJqRwsSeEyaRTUwTlxUqjUymmZpmeI3u62Mv+XWmUzBrpeit7YtB1/r
pTAefv942UcXVX9+MjNVfheGCl18i4ddjwwpPjEslFKDUWeRGj2fnw0JADs=
' GIF:- | some_other_tool - ...
Produces:

See https://imagemagick.org/Usage/files/#inline
ADDITION:
If you want to read one base64 format and write to a variable holding a different base64 form, you can do that with INLINE: in ImageMagick as follows:
Read base64 gif and convert to base64 jpg and save to a variable:
base64jpg=$(convert 'inline:data:image/gif;base64,
R0lGODlhIAAgAPIEAAAAAB6Q/76+vvXes////wAAAAAAAAAAACH5BAEAAAUALAAA
AAAgACAAAAOBWLrc/jDKCYG1NBcwegeaxHkeGD4j+Z1OWl4Yu6mAYAu1ebpwL/OE
YCDA0YWAQuJqRwsSeEyaRTUwTlxUqjUymmZpmeI3u62Mv+XWmUzBrpeit7YtB1/r
pTAefv942UcXVX9+MjNVfheGCl18i4ddjwwpPjEslFKDUWeRGj2fnw0JADs=
' INLINE:JPG:-)
Now read the base64 jpg and convert to PNG:
convert inline:$base64jpg noseguy_b64.png

But JPG does not support transparency, so it is lost when saving to JPG. Thus the background now is black in place of the original transparent.
ADDITION 2:
Convert the GIF to base64 PDF and then convert that to PNG works fine for me.
base64pdf=$(convert 'inline:data:image/gif;base64,
R0lGODlhIAAgAPIEAAAAAB6Q/76+vvXes////wAAAAAAAAAAACH5BAEAAAUALAAA
AAAgACAAAAOBWLrc/jDKCYG1NBcwegeaxHkeGD4j+Z1OWl4Yu6mAYAu1ebpwL/OE
YCDA0YWAQuJqRwsSeEyaRTUwTlxUqjUymmZpmeI3u62Mv+XWmUzBrpeit7YtB1/r
pTAefv942UcXVX9+MjNVfheGCl18i4ddjwwpPjEslFKDUWeRGj2fnw0JADs=
' INLINE:PDF:-)
convert inline:$base64pdf noseguy_b64.png
