(Only) the first "canonical" antiphon of Vespers has a traditional text.

When it is just a new feast - yes.

Thanks, all!

What about Gregorian Mass propers for the new Marian feast on Pentecost Monday? Do we just use those of the Maternity on Oct. 11? Or, do we just use the Common?

In the USA look here.

In Latin the antiphons are :
Introit - Erant discípuli perseverántes unanímiter in oratióne cum María, matre Iesu.
Communion - Núptiae factae sunt in Cana Galilaeae, et erat mater Iesu ibi; tunc fecit inítium signórum Iesus et manifestávit glóriam suam, et credidérunt in eum discípuli eius.
- a dominican setting of the first part here.
or - Ex cruce pendens dixit Iesus discípulo, quem diligébat: Ecce mater tua.

I guess that those are the 'spoken antiphons' (so called, they are usually scriptural snippets which stand alone, phons really), and they never provide one for the Offertory). CDWDS seems never tell us where to find things in the Gregorian treasury. I would look to the Common for singing.
It would certainly be helpful for the Missal to tell us where to find the relevant GR and GS, not just hide the allusion in the intro, which few people read.

Vespers of the feast with OCO-like selection of chants by Czech Dominicans are in this book https://s3.eu-central-1.amazonaws.com/uploads.mangoweb.org/dominikani/prod/uploads/2020/05/vesperale2.pdf , page 448.
(Should the link die one day, try going here and looking for "Večerní chvály II")

It has just a single antiphona super psalmos, because that's how the Dominicans here are used to do chanted Vespers on most days.