What is the ruling on congratulating one another for Eid, shaking hands, and embracing after the Eid prayer?

It was reported from the Companions that they used to congratulate each other on Eid day by saying: "May Allah accept [good deeds] from us and from you." Imams such as Ahmad and Ibn Taymiyyah permitted congratulating on Eid, stating that it is neither a commanded Sunnah nor prohibited. So, whoever does it has a precedent, and whoever leaves it also has a precedent. Sheikh Ibn Uthaymeen permitted congratulating, shaking hands, and embracing after the Eid prayer, considering it among ordinary matters and good customs.