I was told I got the job and I gave references and I haven’t heard anything at all today.

Be patient. Let the process work itself out and for them to do their checklist.

Usually some sort of HR paperwork

Have you heard anything about this since your original post?

employer here. can confirm: takes me about 3-4 days to complete reference check. 4-5 days if using an external contractor to do the due diligence.

send a reminder tomorrow asking if they can confirm they've received the references and if they need anything else from you

good luck!