Thanks for reaching out.
I appreciate the screenshots that you have shared as that is helpful! Would you let us know which theme you are using? As this context will allow us to determine the next best steps to have the logo added to the footer of the store on the mobile version.
If you are unsure about which theme is live on the store, you can navigate to the Theme Editor and select the three dots located towards the top left of the page. I took a screenshot from my test store to show you the section I am referring to:
Looking forward to your response.