Will posting irrelevant content on my domain help or hurt the authority for SEO?

Posting unrelated content on the same domain usually adds little value and can make the site less focused. If you sell social media marketing software, topics like analytics, content planning, and creator workflows fit; unrelated topics are harder to connect to your audience or core pages. I’d keep new posts within a few relevant topic clusters and review older off-topic posts to see whether they should be updated, merged, or removed. What are a couple of topics you’re considering?

It's not likely to actively hurt you (unless you were doing some kind of sneaky re-direct/cloak back to the site's main content).

But any links you were to get to that page you decide to build around the video aren't likely to lift your rankings all that much for the keywords you're trying to rank the rest of their site for. Same goes for whatever traffic you'd get at that domain: would any of those same people be interested in social media marketing software? Traffic for traffic's sake is probably counterproductive unless it's qualified.

Are you able to just host the video on a separate domain or a personal domain (yourname.com) that's divorced from the product you're building? If so, that's what I would do.