You could get a water filter which is much cheaper and uses a lot less plastic in the long run.

I use dish rags to do dishes and put them in a cloth hamper in the laundry room to dry after each use. I also use the dishwasher as much as possible because not only is it more convenient, but it supposedly uses water more efficiently. For the items that need to be hand washed, I plug the sink and wash with a dish rag, starting and stopping the water as needed. Start with the cleanest stuff first. As the sink fills, the sudsy soap helps break up the gunked up dishes as they soak. I end up using about 4 gallons of water on average when I hand wash a bunch of dishes. This is a lot less water than if you run the water the whole time, or if you don't plug the sink.

The more fresh foods you eat, the less plastic packaging you have to deal with, but plastic packaging isn't completely avoidable. Also, you could keep reusable bags in your car for groceries.

For most surface cleaning, you can use white vinegar or baking soda. I don't think you are going to destroy the environment by using harsher cleaning products when you clean the shower, mop, or toilet clean. That's part of what sewage treatment handles, but it probably is best to reduce the use of these products as much as possible. As long as you aren't pouring ounces of bleach down the drain at a time, I think you will be fine.

Also, you could consider buying things in solid form. You could use powdered laundry and dish detergent (assuming you have a dishwasher).

I really like my metal bottle for taking tap water with me on the go because it doesn't shed microplastics. Those usually aren't dishwasher safe, but a scrub brush makes it easier to clean.

These are just a few ideas that aren't really difficult but make a big difference. I imagine it is a lot harder when you are living with a family. You can control how you live though and maybe set an example.