Got an email from Caglar Oner, VP of Engineering (assuming a recruiter email / automated).
Responded same day, heard back from them 2 business days later asking me to complete a 1 hour take home interview. Responded again same day, heard back 4 days later with instructions for the take home test.
Completed it, followed up 2 weeks later after not hearing back, still haven't heard back 1 month after sending it in.
Seems from the other commenters that this is common for Eight Sleep.