The most general place to publish a part, is the “Parts Submit” category here on the forum. Various people have created parts repositories, but none I know of can have parts directly uploaded to them.
If you want to do the work to restructure the part into a “core” part, a PR to the fritzing-parts github repository could get it add. The requirements for that are a bit more stringent than just posting a fzpz file. Even here, you are likely to get feedback from more experienced part file creators about actual or potential problems with the part. There are a lot of ways to have a “broken” part that seem to work, or work, but only for some use cases. I’ll start by pointing to the FritzingCheckPart semi official part validation tool. It will point out some possible problems. A newer version is being developed, but is not ready yet.
FritzingCheckPart will make changes to files during the check, so until you are ready to let it have is own way, run the check on a copy of the part files. It does backup the originals before modifying, but I find it easier to just make a copy of the folder of files, instead of renaming files afterward, if I do not like what it does.