Should I accept this unfunded offer from my dream school or wait for funded offers?
Unless you are independently wealthy, you should never take an unfunded offer for graduate school in mathematics.
Even before the pandemic, some people with a dozen good papers after two successful postdocs - a well above average publication rate - were failing to find jobs.
When I was last broadly applying for academic jobs 10 years ago, the general advice was to send 80-100 applications to jobs you were competitive for in order to have reasonable certainty of getting at least one offer.  Even before the pandemic, there weren't that many jobs in total to apply for, and each job gets more applicants than they did 10 years ago.  (This year is brutal; the only people getting research-oriented jobs will be AMS Sectional plenary lecture candidates (there are roughly 40 per year, total - that's less than the number of Berkeley+Stanford PhDs per year) or better.)
There are even fewer jobs in industry for which a math PhD is a better qualification than several years of experience.
For a more teaching-oriented academic job, the funded position at a lower-ranked graduate school is actually better preparation, because you will be teaching for your funding, and because the undergraduate population at a lower-ranked school is generally more similar to the undergraduate population at most universities than the undergraduate population at a highly-ranked school.
If you borrow money for graduate school, you could end up in a situation where you are unemployed with no means of paying back your loans.  Don't forget education loans cannot be discharged via bankruptcy.
Going to graduate school in math with funding is already a costly decision from the financial point of view, though it's fine if getting to spend a few years doing math is worth it for you (as it was for me).  Going to graduate school in math unfunded is potentially ruinous.