For birthdays there is no blessing in the Mass. The Latin edition of the Book of Blessings has no blessing for birthdays. The USA edition of this liturgical book adds a ceremony for blessing people on their birthdays, but it does not take place in the Mass. (Book of Blessings, isbn 0814618758, Liturgical Press, 1989, Chapter XI Order of Blessing on the Occasion of a Birthday, page 100).
A special blessing for wedding anniversaries is at the back of the book “The Order Of Celebrating Matrimony” (I have the Australian edition: isbn 9781925494051, St Paul’s Publications, 2017). It has:
“THE ORDER OF BLESSING A MARRIED COUPLE WITHIN MASS ON THE ANNIVERSARY OF MARRIAGE
- On the main anniversaries of Marriage, as for example, on the twenty-fifth, fiftieth, or sixtieth anniversary, it is fitting to hold a special remembrance of the Sacrament ….”.
After the homily there is a renewal of “their commitment to live their Marriage in holiness”. Then, if appropriate, there is a blessing of their rings. After the Our Father the prayer “Deliver us …” is omitted and another prayer prayed. There can be a special blessing for the couple at the end of the Mass. The rubrics are: “Then the Priest, with hands extended over the couple, says:”.
So everyone extending their hands is not correct.
[Extracts from the English translation of
The Order of Celebrating Matrimony (c) 2013, International Commission on English in the Liturgy Corporation (ICEL). All rights reserved.]