Having very long experience, my suggestion is to back off a bit on things where you and your partner don't agree on their priority.
Step parenting is like a very complicated dance with lots of possible missteps.
Discus with your partner what is important. Table manners may be one. Bringing empty plates and glasses to the kitchen may be another. Then you can both be involved in encouraging them to do these things.
We used to discuss many things, including how to react to issues from the kids' Mom in a way that did not expose the kids to the conflict or have them feel we were bad mouthing her.
I am sure there are many things you can contribute that are not conflict-inducing. I helped a lot with homework, taught them about nature, ensured they learned about nutrition, and stepped in to help them understand why calling each other "gay" as an insult was not appropriate.
We had a family meal every night when we could, and I am convinced that helped with many things.
Making beds, not so much. Taking dishes from the table to the kitchen, yes.
If you take into account they are kids and have two different standards to learn, it helps.
I hope that doesn't sound preachy. I didn't mean it that way.
My heart about bursts with love and I am more than proud of my stepsons and grandchildren. It was all worth it.