Is it permissible to publish pictures of someone who has recently embraced Islam, or memorized the Quran, or performed a good deed, with the intention of attracting people to offer congratulations and supplications, while mentioning that they did not find anyone to congratulate them?

There is nothing that prohibits this action, but the method is inappropriate and involves artificiality to solicit interaction. It often originates from those who exploit images for personal gain. It suffices for the publisher to say: "Pray for so-and-so for steadfastness, for he has embraced Islam," or "Congratulate so-and-so, for he has memorized the Quran," while exercising caution in publishing images of one who has memorized the Quran due to the potential for fitna (temptation/strife), riya (ostentation), and ghurur (vanity).