The phrase to test in this question is "at home." Check whether the rules about shoes stop at the front door by reading what the written guidance says.
The answer is no
NIDDK instructs people with diabetes: "Do not walk barefoot or in just socks – even when you are indoors." The words "even when you are indoors" were written for exactly your situation, so the home exception you were hoping for does not exist in that sentence.
Where the guidance repeats itself
The American Diabetes Association points the same way for the warm season. It says to refrain from going barefoot, wearing flip flops, or other open shoes in the warmer months. Two organizations, two different seasons and settings, one direction.
The full pages are worth reading in their own words. MedlinePlus covers the diabetic foot as a topic, and the CDC has a clinical page on promoting foot health. The American Diabetes Association also publishes foot care tips for people with diabetes, and the CDC keeps a page titled your feet and diabetes.
What to confirm, and with whom
Ask your doctor or podiatrist what indoor footwear they want you in, since the guidance above names what to avoid and leaves the choice of shoe to you and your care team. Bring up house slippers specifically, because the NIDDK wording lists socks alone as a problem too. For readers in and around Itasca, the question belongs in your next diabetic foot exam.
The clause people skip
Socks are in the sentence. "Barefoot or in just socks" puts both in the same instruction, so socks do not count as footwear under it.