Happen to have an interest in this name as it was on my own girls list (had a DS in the end!)
Not at all boring, it's a beautiful, simple, elegant and timeless name imo 😍it often makes "classic" name lists for a reason (and I personally only know a few of very differing ages),
There are hardly "legions" of Eve's and no it hasn't been "done to death" (at least in England and Wales - a simple look at statistics will tell people that, it's never even quite made the top 50 for goodness sake and it's historically usually stayed outside the Top 100 including at the present moment). An Eve born today will likely be the only one in a smaller school - possibly a couple of others in bigger schools but that can happen with any name 🤔
An issue might be if she/her peers decided to use the nn "Evie" . In 1999 the film The Mummy came out (main character Evelyn "Evie") followed by the film Pearl Harbour in 2001 (main character Evelyn). Evie and Evelyn (who often seem to be known as "Evie") shot up the charts and are only gradually decreasing now - Evelyn the more slowly since that has also been boosted by the 100 year naming rule (my own Great Grandmother was an Evelyn!).
Eva is kind of a special case, as although it has been greatly boosted by the popularity of Evie and Evelyn, it's a much more "classic" name as it's so multicultural and is used by all ages in other countries. So I suspect it might stay reasonably well used even as Evelyn and Evie eventually fall, since many people look for multicultural names now.
Anyway, long story short OP- do you care that there will be multiple Evie/Evelyn/Eva's in your DD's school? (check the ONS stats for your area) There may even be several in her class. Could be confusing to teachers/peers if your Eve doesn't stand out for other reasons (than her name). If you aren't bothered by that, then I say go for it - Eve is such a lovely name.