I see your valuable contributions quite regularly here; thanks for those.
Thanks for asking first, as well.
The SE network has a fairly clear policy on self-promotion, which you should look at.
Limits for self-promotion in answers
What signifies "Good" self promotion? (or: Self Promotion Part Infinity)
For more than you'd care to read: https://meta.stackexchange.com/search?q=self+promotion
Where there's a question to which 'my software solves that problem' would be an answer or part of an answer, you're allowed to mention software you made or helped make or are otherwise associated with -- as long as you clearly identify your association each time (saying 'my package ...' is usually sufficient). [However, as gung notes, the sort of question to which that would be a complete answer is fairly likely to be off topic here. On the other hand, there can be answers to which some mention of software would fit quite well.]
What does tend to be frowned on is anything that looks like an attempt to advertise*. For commercial products there are ads, and for open software there's also a program that operates to 'get the word out'.
* (and I know that on SO in particular, asking and answering your own question which includes a link to software you were involved with is highly likely to draw the ire of moderators or other involved users; in your case it's probably surviving on the basis that you wrote it in response to your original question, rather than posting the question in order to give that response)
On the specifics of your question -
should one repost a question-and-answer from there to here. The broad principle is that reposting of questions to multiple places should be avoided
Please note, however, that cross-posting is not encouraged on SE sites. Choose one best location to post your question. Later, if it proves better suited on another site, it can be migrated.
There's some flexibility -- in particular, where one site is likely to offer different kinds of answers, the same question might fruitfully appear on both - we have tolerated some reposted questions before. But since here the purpose is to display exactly the same answer, I'd say that 'different takes on the problem' doesn't apply, and the principle stated in the help will be the one that's more relevant.
should one repost that particular question - my feeling would be "probably no", since it would very likely be closed as off topic (even aside all the previous considerations).