Can you say that you reject the null at the 95% level? I know that you reject the null at the 5% significance level. But I read someone writing that they reject at the 95% level. I assume the confidence level. But can you technically say that?

You can* but should not.
You're conflating language of confidence intervals with hypothesis tests. The level of a test is the significance level. "Confidence" levels (coverage) is a property of confidence intervals. There are connections between them but they are NOT the same thing and you should not mix terminology between them.
If you're performing hypothesis tests, use the terminology of hypothesis tests. If you're calculating confidence intervals use the terminology of confidence intervals. What could be easier?
* (I sure can't stop you, these space lasers are useless)
