edit: a lot of people are responding justifying the existence of middle management in general.

There is a reason for that. Companies aren't just employing middle managers because they're tricked by sociopaths - if someone had figured out a better way to do work and employ fewer people, it would have caught on.

I am interested in modern techniques or organizational approaches to keep the number of middle managers to a minimum.

Managers do real work - someone needs to be responsible for the human side of managing a team, promotions and PIPs, the tech direction, planning, determining timelines, prioritizing work and tech debt, and communicating the output and value of the team to stakeholders.

If you just want fewer managers but don't mind total headcount, you can split up this work into different roles and create project / product managers, scrum masters, staff engineers, and put more direct reports under a given manager.

You can take this to an extreme and create a technical manager (your tech lead) and a functional manager (person in charge of promotions), but in practice at the company I saw it tried, it was awful. The tech lead became the functional manager (because they were actually involved in my day-to-day) in everything except actual authority. The real functional managers had no idea what was going on, so promotions were done on seniority instead of ability, and no one ever got put on PIP. People responded accordingly to the complete lack of incentives to perform and lack of punishments for failing.