I see what you're saying. It is a dilemma. To me neither the cause nor solution to that lie specifically in philosophy or stoicism, but rather in Buddhism. Existence is an illusion, none of it really matters or means anything but simultaneously it does all matter. Because what you do and how you handle it determines whether or not you will ever escape it and how much you will suffer in the meantime.

Stoics, as far as I've read, kind of touch on the existential crisis a bit, but the reality is we exist and therefore we suffer but we only suffer and only suffer so greatly because we think we exist. It can seem very convoluted and took me a long time to come around to but Buddha even said that a "dispassion for life" is one of the many steps to enlightenment and ultimately ending rebirth. Eventually you realize it is futile. You cannot escape the suffering, it is part of the world and part of nature, but you can learn and train yourself to escape your perception of suffering. There is meaning in living like this, but once again that meaning is just part of the overall illusion.

The bottom line, really, is just practice love and compassion. The rest sorts itself out but eventually most of us have to make a conscious choice to wake up, and only then do we see the illusion.