Can a crashed iphone be jailbroken

I have an old iPhone SE first edition, that recently just crashed. I have a back up for it, but from what I'm learning, I would actually have to update it to iOS 15, to make it workable, before I can even jailbreak it. Is that correct? Is there any way to restore the device to its iOS 13, or even an earlier version that I have on an iPhone back up on my Mac?

I would like to attempt to jailbreak this phone, but I'm not sure how to get started, and I'm not sure how it will run on iOS 15 anyway.