I don’t think you are overreacting and I think you have every right to feel unappreciated. Everyone in the house should be pulling their weight and doing their fair share around the home.
Have you suggested creating household rules so your family can help you with the chores? You would need your partner to be united with you on these changes, so they support you and help you to enforce the house rules.
Start with a family meeting so you can voice your feelings so everyone knows how you feel. Discuss the chores that you need help with and get all the family involved with how they can help. Sometimes when children are involved with making lists and charts they become more invested in the whole scheme. Perhaps ask them to design a chores chart and stick it on the fridge so everyone can see it and everyone knows what they need to do. Another incentive is to pay them pocket money to help with the chores. No chores, no money.
As for the backchat and rudeness, I would suggest your partner deals with this if it is their children that are disrespectful to you. The biological parent should discipline the children and let the children know that if they disrespect you then they are disrespecting them also and that is not okay. A united front comes across so much better so the children know they are dealing with you as 2 parents and not 2 individuals.
Maybe it should also be your partner’s responsibility to check on their children’s homework and to make sure they are completing it. You could suggest that doing homework before watching tv or playing on their phones or computers is one of the house rules.
Sometimes children just need structure and to be organised in what they need to do. Once a routine is in place and with your partner supporting you I feel it could make you feel better and hopefully feel more appreciated. It would also create some ‘you’ time and we all deserve that. I hope this advice helps and creates an easier family life for you.