Excel.
Unless your project is huge (multi billion), requirements gathering is mostly about the BA and others understanding how something will be used. So it's human brain work. Excel is a nice way to keep and monitor lists of requirements and link then together, add dates etc.
It's something everyone can operate (stakeholders to Devs, without a new license or needing to be taught it).
Ive seen a LOT of projects use shiney clever solutions and they always either fall back to people's brains or fall on their face because someone didn't complete the dependency matrix overview page in exactly the way the software needed etc.