I disagree. Many hard working people are practically invisible and get kicked when there are layoffs. I am not linking layoffs directly to invisibility, but I'd argue that promoting yourself and being known and liked by the important people at your job gives your position more security.

As an example, if you often hop on calls and assist team members, let it be known to your manager. That's self promotion.

Collaborate with your PO. If your team presents their work to other stakeholders regularly, volunteer to present. These are different ways to self promote by simply doing your job.

The rest won’t always follow, but doing good work is the first and most important step.

For me the breakthrough in my career was making sure the right person knew I was interested in a particular project, but that would have meant nothing if I hadn’t already built a reputation for good work.

Sadly the game doesn't work like that.

That's served me well for 25 years in the industry. I don't think this approach works everywhere - the larger the organization, the more you need to play this game. Since I hate that game, I've stayed away from orgs like that on purpose, done well, and have been happy.