Just from random experience myself, I got into skipping as easy to do in back yard (couldn't do more than a few minutes at first at all! Also do a couple of times a week at first to help legs become accustomed) - I now find it extremely good for a quick cardio. I'd count sets of 20 skips to 100, then try to see how many sets I could get to!
Trust me I'm a dr on bbc had some simple muscle strengthening things to try at home on their website.
Katy Bowman of Katy says (Nutritious movement) has lots of ideas and tips but it can take a while to wade through it all as there's just so much! She's into swinging (
not that sort) so a door bar could be good.
I think stairs can be useful; I used to step up and down pushing weights into the air (no idea if good or not!).
If you careful about posture etc, things like scrubbing the floor can be an excellent work out! Lynne Robson's pilates had a really technical app (do pay but like a mini book with videos) to explain lots about basic posture, as does Katy Bowman.
I also like to do handstands against the wall. Seems to help upper body strength and my wrists. (Katy has a way of learning how to in a door way)
It is possible to turn your home into a gym with little to no extra equipment. Pilates ball could be helpful too (Google things to do on that)