She is Mekudeshet for sure even without Harei At and he does not have to give the ring again.
Explanation:
The Gemara in Kiddushin 12b: He told her watch this coin for me and then later he said let’s use this coin to get married (to do Kiddushin). If he said it as he gave her the coin and she accepted it then she is Mekudeshet but if he said it later then if she agrees then they are married but if not then no. What does it mean ‘she agreed’? If she spoke it out ‘Yes’ or ‘No’ then in the first case even if she said ‘no’ she is married, but she said “No”. Agreeing means she said ‘Yes’ and no agreeing is keeping is if she keeps quiet.
It seems from the is Gemara that if the Chatan tells the Kallah after he gave her the ring “Harei At” the Kiddushin depends if she expresses her consent, meaning she says ‘Yes” but if she quietly accepts it, she is not married. However, she does not need to go back and redo it. Nowadays though the Kallah never says “Yes I will marry you.”
So, it is in the Shulchan Aruch EH 28:4: If he gave her something to watch and then he said take this be makeshift to me with it, it depends. If he said it before he gave it to her and she took it even quietly she is Mekudeshet. If she is already watching it and then he says it, and she is quiet it meaningless, but if she says “Yes!” She Is Mekudeshet.
The Rashba (Kiddushin Daf 6) is of the opinion the if he gave her money without saying anything and then he says “Harei At” and he had in mind it was for Kiddushin she is not Mekudeshet even if he said out the words. He must take the money back and then give it to her properly. So rules the Rema there.
The Taz asks on the Rema from the Shulchan Aruch and he doesn’t answer.
[The Sefer HaMakneh also rules that he needs a do-over and he adds that even if gives her the ring and says, “Harei At Mekudeshet,” within ‘Toch Kdei Dibbur” within three seconds after he gives it even then it doesn’t work because we never find when someone buys something that after he gives the merchandise right away he can say, ”Wait a second…” Therefore, one also must be sure that the Chatan finishes his sentence before giving the ring.
The Avnei Miluim and R Akiva Eiger ask that in Choshen Mishpat we do say that they are allowed to nullify the transaction within Toch Kdei Dibbur, so too here it would work.]
The Avnei Miluim answers the Taz’s question on the Rema that the Rema is only stringent when the Chatan just gives the Kallah something without any explanation, therefore she assumes it to be a gift and therefore it isn’t good and he must redo everything since she took it as a gift. The Shulchan Aruch is talking about when he told her to watch it, therefore she does not make a Kinyan and it is still his, therefore, it works for him say Harei At after. So, it would still seem they would need to have a do-over.
There is Mishna in Maaser Sheini4:7 If a man was speaking to a woman about marriage or divorce and he gives her a ring or a Get and he doesn’t explain. R’ Yossi says it works and R; Yehuda says he needs to speak out what he is doing.
According to R’ Yossi if they are discussing marriage and he gives her a ring she is Mekudeshet.
So rules the Shulchan Aruch 27:1
In our case where the Chatan and the Kallah are in a Wedding hall wearing wedding clothes and standing under the Chuppah, it would be considered as if he was discussing getting married and could be even more so. Therefore, even if the Chatan forgot to say anything it is Kiddushin Bdi Avad and the Rav was correct to just continue the Chatunah.