I work for a large tech company. I'm paying about $16k a year after monthly premiums and annual deductibles for a family of 3. (All but $6500 of that is pre-tax).

It's not at all uncommon for companies, even small ones, to pay 100% for the employee. Paying for spouses and children is much less common.

Most companies offer pretty good health insurance immediately.

Usually there are options like Kaiser in CA that are all inclusive similar to what you’d see in Europe. Some offer cheaper options. Some offer options that include health savings contributions from the employer to offset high deductibles.

How do these plans work when you lose your ability to work, like in an accident or longer sickness? Do companies keep you employed? Do you still get to keep the health insurance for a time after this?

I work for Twitter and the health coverage is quite good. Max annual out of pocket is $2000 and mental health is covered 90% from the first dollar.

I pay $1000/year for my policy.