There are lots of different singularity definitions on wikipedia, most focus on 'intelligence' (eg "an upgradable intelligent agent will eventually enter a 'runaway reaction' of self-improvement cycles, each new and more intelligent generation appearing more and more rapidly"). I think focusing on what 'intelligence' really means, or whether any model is 'truly' intelligent can be be a bit of a distraction. So I just emphasized capabilities in a rather generic sense instead.
It's clear that LLMs can compete with humans on many tasks (coding, creative writing, medical diagnosis, psychotherapy,...), and it is conceivable that they may surpass most humans on those tasks some day. If we have models that can outperform most or all humans on important professional and everyday tasks, and also produce new models that perform even better, maybe at an accelerating rate, through means that are ultimately not interpretable for us, I'd say that's pretty close to a singularity, regardless of whether they're 'truly' intelligent. Even more so if they pass a duck test (walks like a duck, quacks like a duck,...).