I suspect this answer will not be very satisfying to you, but it is in some sense the true answer so someone should provide it:

There are a great many possible causes in the world, and EA is focused on things which are (plausibly) the most effective in the world. By their nature only a small fraction of all causes are plausible candidates for the most effective, so we should expect most causes to not be EA causes. If you had some concrete arguments for why biodiversity might meet such a stringent standard, people could consider them, but in their absence the 'default' is for something to not be an EA cause.

In particular, in addition to some argument as to why having many species is very important, you might want some sort of comparison to:

• Existential risk work, which aims at preventing the irreversible extinction of all species.*
• Wild Animal Welfare work, which regards wild animals as maybe having net negative lives, and hence their extinction might be good (if this was by reducing the total number of animals).

* as a first approximation

Upvoted because I think that this should not be downvoted without comment. However I think OP will get more engagement and generate a fuller respose here if:

• The arguments that there is a mass extinction going on are summarized rather than linked to.
• Some facts about funding levels are given. E.g. how much £ overall goes to eco / wildlife / conservation charities overall versus EA causes. Otherwise some may respond that funding from EA sources is not required, or there are more neglected priorities.
• The case for impact and why biodiversity loss is worse than other causes the community focuses on. E.g. there will be those happy to concede that it is bad, but meaningless in the event of x-risks coming to pass.

Note: I am sympathetic generally to the need for a diversity of causes, I'm just pointing out some elements I'd expect to see in an argument which proved persuasive.

Partially the answer to this question is that biodiversity protection involves a wide variety of interventions, some presumably effective, some not, and across all those interventions it is not clear how neglected the cause area actually is.

However, a bigger reason might be the inherent conflict between traditional environmental protection, focusing on biodiversity, and the animal welfare/liberation movement. The latter is a lot more prevalent in effective altruism, through organizations like Animal Charity Evaluators and Wild Animal Initiative. There are some sources I can recommend to help clarify the nature of this conflict, starting with "A Triangular Affair" by J Baird Callicott, and "In Nature's Interests?" by Gary Varner, but briefly: if wild animals are moral patients with rights, it is not clear that their status as this-or-that-endangered-species matters very much, and vice versa. In EA, we tend to focus on the experience of animals as a neglected source of suffering, and that does trade off against biodiversity concerns.

Finally, the philosophical case for why we should value biodiversity isn't clear-cut, although I certainly share your intuitions about it! This is an essay from a biologist in the community about what might be valuable about biodiversity and how mainstream environmentalism might be getting it wrong: https://eukaryotewritesblog.com/2018/05/27/biodiversity-for-heretics/

 

I was hoping to see some more answers by now, but seeing none I'll provide some initial points that I expect people who are more familiar with the field could flesh out much better than I. I'm not familiar with the full case for biodiversity, but just based on generic reasoning about cause areas in general, I'd suspect some of the major reasons EAs do not seem to consider it as important as factory farming, wild animal welfare, or even climate change (to name a few environmentally-oriented cause areas) include:

1. It's unclear how significant the extrinsic, welfare-oriented value of biodiversity even is. Put most bluntly, "if some random frog species goes extinct, so what?" I understand there are arguments like "what if this species proves to be very useful for e.g., pharmaceuticals or the broader ecosystem",  but I'd want to see some quantification and comparison with other cause areas. Is it worse for the last 100 fish of some random species to die (=> extinction) than for 100 chickens to suffer factory farming conditions? Maybe, but I could also definitely make the case for the opposite conclusion. And as a few other answers/comments pointed out, it definitely seems to be much smaller in significance than human X-risks.
2. (On a smaller note since I am not very familiar with this field, I'll add that it's a bit difficult to understand what all of the charts, figures, and bullet points on the link you shared amount to. Lots of things may qualify as endangered, but how many things actually go extinct? How is this impacting the environment? It's all just much more difficult to neatly quantify the situation than it is to put a probability estimate on X-risk, preventable mortality estimate for malaria, number of animals in factory farming conditions, etc.)
3. It's unclear whether there are cost-effective interventions (in conjunction with point 4): if you would like to propose/list some, that would help, but if it's the case that vast numbers of these species are going extinct/becoming endangered due to a wide number of environmental changes, it seems more difficult to identify highly cost-effective interventions (in contrast to, e.g., bed nets for malaria, surgery for trachoma).
4. Some (non-EA) organizations are already working on the field of biodiversity and conservation. This certainly doesn't mean that it's already fully saturated, but in order to determine whether there are cost-effective interventions that need funding, one must also consider what kinds of efforts/funding already exist.

In the end, this isn't to say that biodiversity is necessarily "unimportant" and completely intractable, but given the combined issues surrounding comparative importance, tractability, and neglectedness I don't know if it's really an area where EA would have a comparative advantage in relative to e.g., AI safety/alignment (which itself may prove very impactful for the environment and many other problems), cost-effective health interventions (e.g., bed nets, deworming), and general long-termism. I would be willing to read an argument for why it is overly neglected, but I haven't seen that argument made yet.