Almost like as if people are looking to hire a one-man army to handle the entire department.
Not a hiring manager or a recruiter, but that's exactly what full stack entails in most places. A company that's looking for full stack is likely to be small and require wide skills. Otherwise, they would have dedicated teams for frontend/backend/devops.
If you want to avoid that, I'd recommend building a focus on frontend or backend (or devops/infra/sysadmin) depending on what you like more. I decided early on that I wanted to do backend, and I focused on projects and job applications that complimented my skillset. In my career, I've done work all across the stack (infra, frontend, backend) but I'd never call myself fullstack.
I like backend because it encompasses anything that's not UI. Terminal applications, games, web APIs, FOSS contributions... All transferrable to backend skills. The rest of it is learning whatever web framework your company uses to build their services.