HoldTheTomatoesPlz's journey

I recently interviewed with a company in the US and have been in the process for about six weeks now. I completed two interviews, a take-home project to assess my problem-solving skills, a third interview, and even toured their warehouse and facilities. After that, I had a fourth interview and sent over multiple references. It’s been 13 days since I provided those references, and I've only received one email confirming their receipt about 10 days ago. I initially thought it was best to wait until after the 4th of July to follow up, but now it's approaching two weeks without any updates. I’ve checked in with my references, and they mentioned they were contacted early last week. I'm unsure about the next steps and would appreciate any advice on how to send a follow-up email without seeming too pushy.