How do you get users for a reverse job board?

That's kind of a chicken and egg problem when starting a multi-sided market. The value for companies depends on (and increases by) the number of job hunters, and, vice versa, the value for job hunters depends on the number of companies. Maybe it's helpful to get some inspiration from how other platforms started. A common strategy that I personally observed is to subsidize one side of the market or provide it with some monetary incentives to attract the other side (e.g., no/lower fees for one side if it's a paid service).

Though they may be other strategies, like faking one side. Faking does not mean creating fake profiles to deceive users - that would probably result in a bad service experience and unmet expectations. Instead, a faking strategy could consist of manually searching and forwarding suitable job listings from companies to job hunters even though the companies are not registered on the job board (yet).

Probably by doing the first steps manually, reaching out to companies or users when there is an offer available. Without traffic, this needs to be done by you.

I'm also building a reverse job board. Also, I have a regular job board for backend engineers (getbackendjobs)

I can guarantee you that LinkedIn is the number one traffic for anything related to jobs.

Also, using programmatic SEO can be very helpful in the long term.

Run an ad on linkedin, email a bunch of people. Send them looms.

You may publish opennings on Linkedin with different job titles and descriptions. Application link can be a specific landing page describes benefits to your product with a quick onboarding scenario.