I’ve been to a Messianic synagogue that celebrates the L-rd’s Supper only once a year - at Passover. I don’t think I would call it “eucharistic communion” (as stated in the OP), though.
Other synagogues (messianic, of course) celebrate it more often, but I’ve not seen any where it is common to have it on a weekly basis. I’ve never heard of any specific requirements regarding when/how often it is to be observed - other than Passover, naturally. I believe that matter is left to the rabbi to decide. Matza and wine or grape juice is used. It is a symbolic representation of what Messiah did by giving/sacrificing Himself for our redemption.
Anytime I’ve celebrated the L-rd’s Supper, there is always an admonition to carefully examine one’s self. (I Cor.11:26-32)
26 For as often as you eat this bread and drink the cup, you proclaim the death of the Lord until he comes.
27 Therefore whoever eats the bread or drinks the cup of the Lord unworthily will have to answer for the body and blood of the Lord.
28 A person should examine himself, and so eat the bread and drink the cup.
29 For anyone who eats and drinks without discerning the body, eats and drinks judgment on himself.
30 That is why many among you are ill and infirm, and a considerable number are dying.
31 If we discerned ourselves, we would not be under judgment;
32 but since we are judged by (the) Lord, we are being disciplined so that we may not be condemned along with the world.
shalom