In Peirce we have the notion of firstness which is a phenomena as it is purely in itself with no reference to anything else. Now of course what enables a moment of firstness is contextual. My experience of love is made possible by meeting my wife, living in a culture in which love of a sort is given a sense, a set of practices, and so forth. But the absolute phenomena of love is something purely singular. Being, although rarely discussed by Peirce, is often seen as something prior to firstness which enables firstness. (Kelly Parker has argued that Peirce adopts a nearly neo-Platonic cosmology of Being)Not by itself. Ereignis needs a clearing, in which things, cultures, practices, etc., show up.
What is key is that Being isn’t simply a collection of events but a transcendental move of what makes the events possible as the kind of events they are.
The difference between Peirce and Heidegger is that Peirce isn’t only doing phenomenology. That is he sees phenomenology as one category within existence. Whereas Heidegger is doing phenomenology (although with his move to “thinking” he clearly expands beyond pure phenomenology). The question then becomes what makes not just phenomena but all things ontically what they are. Is Heidegger’s Ereignis up to the task? I don’t think it is.