It turns out my first campaign will be Curse of Strahd (5e). I'd like to play a vampire hunter who is knowledgeable about supernatural monsters as a matter of profession. Furthermore, I have a vampire written in his backstory and am toying with the idea of associating the vampire with a coven, although I have no idea whether the concept of vampire covens exist in the DnD-verse, and if they did, what their names and properties are.

Is there a spoiler-free source to read up on supernatural monsters, their cultural nuances in lore as well as generalized traits and abilities?

Obviously, nothing that contains information which would detract in any fashion from the campaign.

What counts as a spoiler depends on your table...

The best source for lore on monsters for DnD 5e is the aptly-named Monster Manual book. It contains varyingly long lore dumps ranging from a couple of paragraphs to short stories. The descriptions are often quite interesting! Each is also accompanied by the stat block of the monster.

Since you're playing Curse of Strahd, the module's book itself will contain lots of background information that the GM may or may not allow you to view. Outside the particular scope of vampires, other DnD 5e books also include monster or location lore as a part of their content. You can look up books like Mordenkainen's Tome of Foes or Volo's Guide to Monsters to get access to more and deeper lore dumps.

Whether the lore or the stat block are "open information" varies between different tables. Our table has usually run under the assumption that most of the lore presented in the book is reasonably common knowledge that has been passed on to our heroes through folklore, their earlier careers or other experience. Stat blocks are usually considered to be spoilers, but your mileage may vary.

...so ask your GM to meet you half-way

Ultimately, it's the wisest to ask your GM to point you to the lore they intend to use. This not only ensures that the GM can only provide you with the information that doesn't spoil the campaign, but also ensures that the information given is not misleading in the event the GM decides to detract from the more established sources of monster lore.

Finally, given the nature of the campaign, I'd avoid playing an experienced vampire hunter without strong and explicit approval of the rest of the group. The gothic horror atmosphere of the campaign is supposed to flood the players with grim mystery, that might be diluted were your character to claim a specialized knowledge in the workings of vampires.

The Monster Manual

The most obvious place to look for generic information on vampires would be the Monster Manual. It contains some flavour information on vampires (p. 295) as well as their stat block and lair actions (pp. 296-297). I am not aware of any other generic information about vampires for 5e outside of that.

However, even though there won't be anything specific to Curse of Strahd in there, given that you say you'd like to play a vampire hunter, I'm going to assume that you are a player, not the DM. In this case, looking at the stat block of a monster may not be something your DM would be happy with, so it might be best to ask them about this with your intentions. It might be that they're happy for you to read the flavour entry, but not look at the stat block, for example.

As for covens, in D&D, as far as I am aware, covens are more of a Hag's thing (Monster Manual, p. 176), so that detail would again be up to your DM as to whether covens of vampires exist within their game.

There isn't really any single "D&D-verse". There are many, many different campaign settings, both published and homebrew, and there's no guarantee that the lore of one will match up with the lore of another. The Monster Manual is the source of information which is most likely to be consistent across most D&D settings, but, even then, any individual DM is free to overrule published materials in the context of their own campaign.

The only reliable guide, then, is to ask your DM. They may point you to published materials which they feel will accurately describe their campaign setting, or they may directly provide you with information that your character knows (or thinks they know!) about the world around them.

On the specific matter of vampire covens, they're not a common thing in most D&D settings, but another advantage of the "ask your DM" approach is that you can turn it around and tell them, "I think it would be really cool if there were vampire covens in the game. Can we (or you) add them to the setting?"