What is the brown and yellow goop coming from my vents?

What people tried

Every workaround mentioned in the threads below. We haven’t tested any of them — and nobody here is claiming they worked.

1. 1
   Hiring an HVAC company to inspect ducts and recommend duct cleaning, sanitizing, or air scrubbers
2. 2
   Pouring hot water and baking soda on the carpet
3. 3
   Renting a carpet cleaner to extract dirty water stains
4. 4
   Replacing rusty metal register covers with new or plastic ones
5. 5
   Using a dehumidifier and moisture meter to dry out affected areas
6. 6
   Texting the window company
7. 7
   Inspecting the debris for insect parts
8. 8
   Hiring a pest control company to inspect the issue

In their words

Unedited, grouped by where they were said, most upvoted first within each place, each linked to the thread it came from.