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. It is noteworthy that the Monster Manual contains a backstory block for Strahd himself, so there is definitely some minor campaign spoilers there too. Ask your GM to be sure.

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 deviate 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?"

The Curse of Strahd's default setting is Barovia, a location in the campaign setting known as Ravenloft. Ravenloft is primarily a Gothic horror setting, and has a somewhat unique lore unlike most other D&D settings. During the AD&D 2nd edition period (the setting was first created in 1990), most of the "default" creatures were slightly modified one way or another to reflect the setting's unique character. Some of those modifications were mechanical, and a lot were in terms of lore. As such, generic "Monster Manual" type books might not really work for what you want to do.

As a solution, you might consider reading old Ravenloft sourcebooks (the AD&D 2e mechanics are going to be different enough that they would most likely not ruin the 5e module). For example, consider Van Richten's Guide to Vampires; a book written by the in-game character, famous Dr. Rudolph Van Richten. Alternatively, you might look at the Ravenloft series of novels.

However, it is critical that you consult your DM before even reading these materials; horror is a very important part of this setting and knowing too much might really harm the mood of the game. So please make sure she/he gives the green light first.

Old sourcebooks and D&D wikis

Monster sourcebooks

TSR released a lot of highly specific and detailed sourcebooks during the AD&D 2nd edition era, in some cases dedicating entire sourcebooks to individual creature types. Other sourcebooks from various editions provide additional detail.

Ravenloft-specific sources include Van Richten's Guide to Vampires (1991), Children of the Night: Vampires (1996), and Van Richten's Monster Hunter's Compendium Vol. 1 (1999). The Ravenloft Campaign Setting (2001) likewise details vampires, though beware that learning more about your DM's setting than they do will put you out of sync.

Undead-specific sourcebooks include Libris Mortis (2004) and Open Grave (2009), while the 5e Monster Manual (2014) will detail vampires as they are in D&D 5th edition, and the 3.5 Monster Manual (2003) will give you some extended vampire lore.

In particular, the 3.5 Monster Manual asserts that vampires might be encountered solitary, in pairs, in gangs of 3-5. or in a troupe of 1-2 with 2-5 weaker vampire spawn.

Wikis

D&D wikis have the issue that the most popular are repositories for fan-made homebrew content rather than encyclopedias of canon, and this is not always obvious. However, there are several wikis specifically for D&D world lore, mainly campaign setting-specific:

• 
  Mistipedia, the Ravenloft wiki, has a particularly large category on the vampire.


• The Forgotten Realms Wiki is the largest D&D wiki and is full of lore on individual creatures, such as the entry on the vampire.


• 
  Wikipedia frequently has well-researched articles on major D&D topics, such as D&D's version of the vampire.


• The D&D Lore Wiki has setting-non-specific information on various creatures, but it has relatively few pages and and most major creatures such as the vampire lack a thorough article.

Other

A DM is free to invent new things without any precedent in canon lore to help your character concept. It may help to research sources of real-world folklore.