You can use session_state to store information if you need to extend the memory of buttons. I just recorded a tutorial if you want to check it out. Session State Introduction
You can add a callback function to your form submit button like this:
if 'submitted' not in st.session_state:
st.session_state.submitted = False
def update():
st.session_state.submitted = True
# Your Form Here
st.form_submit_button('Submit', on_click=update)
if st.session_state.submitted:
st.write('Form submitted')