TPRO is not directly supported. You should be able to set it in scripting via
$set(_id3:TPRO,2020 Someone). Note that Picard will not read this back, so you will not see it when loading the file. Also note that according to ID3 spec
TPRO is very specifically for the the production copyright holder f the original audio, not really the producer of this recording. As such the spec expects this to start with a year number, and software should then display it as e.g. “Produced ℗ 2020 Someone”.
producer itself will be written to
TIPL:producer (ID3v2.4) or
IPLS:producer (ID3v2.3) by Picard.
For TPE2 Picard uses
albumartist, TENC is
See also https://picard-docs.musicbrainz.org/en/appendices/tag_mapping.html