This sometimes happens with a small number of cases (events in survival analysis) that won't support the number of coefficients needed for a model with interactions. Based on your description, that doesn't seem to be the situation here. You have a reasonable number of events in each of the treatment/education combinations, and an overall ratio of events to predictors that seems OK.

I note that education level 2 showed a much different pattern in number of events as a function of intervention than the other two education levels. If the intervention assignments were adequately balanced within each of the education levels by the randomization, then there might well be a substantial interaction (although why the intermediate education level is different from the others might be hard to understand*).

It's possible that there are some correlations of the covariates with education level that are inflating the individual coefficient standard errors. Examine not only the individual coefficient standard errors but also the entire variance-covariance matrix of the predictor estimates (via the vcov() function for many R model types). Converting it to a correlation matrix can help identify which coefficient estimates have high (typically negative) correlations, particularly when there are interaction terms.

It's possible that the inflated individual standard errors won't matter in the overall assessment of your results. With the interaction, you no longer have a single coefficient for the intervention. The association of the intervention with outcome evidently depends on education level. You need to combine information among all education levels with some type of "anova" to judge whether there is any association at all. I find the "chunk" Wald tests provided by the anova() function in the R rms package, for objects created with that package, to be the easiest to understand. In those combined tests, negative covariances among coefficient estimates can counteract the apparently large variances of the individual estimates.

*I don't think that this is a problem here, but for later visitors to this page: the common mistake of using numeric labels for more than 2 levels of a categorical factor can lead (often by default) to that factor being treated as a linear numeric predictor rather than a categorical predictor. In a case like this, with those having an intermediate level evidently responding differently to the intervention than those with the other levels, linear numeric modeling wouldn't work well.