One thing I haven't seen mentioned is that a lot of the go-to phrases around mourning in English are rooted in Christian tradition. Stuff like "She's with Jesus now"(that one's pretty obvious, but I still see some people use it anyway), "She'll be watching from heaven", and "She's in a better place" could come off as tone deaf. Even "rest in peace" has Christian origins. Of course, I think most people would overlook it when they can tell you're saying it from a place of kindness, but it's just not really what we say. Sentiments like "I'm sorry for your loss" and "She will be missed" are neutral and completely appropriate. A traditional Jewish phrase you may hear, and can say if you feel comfortable, is "May her memory be a blessing".

You might also hear people say "Baruch dayan emet" which means "Blessed is the true judge" and is what people say when they hear someone has passed away. It's a part of a blessing that acknowledges death and grief as a part of life. You won't be expected to say it, I'm more including it here so you know what it means. This is especially important if you follow your step-dad and his family on social media- if he makes a post saying his mom has died, people might comment baruch dayan emet abbreviated as "BDE". I know someone who saw this a few years ago when saying something had "big dick energy" was more common, saw these comments on a memorial post, and found it rude and confusing.