Does my rate match the salary?

Sure, but since the absolute majority of Germans only know and experience it that way, it is more like a bicycle chain than a serious consideration/calculation.

If the employer did not have to pay about half of the health insurance, he might possibly add it as salary. The employer always calculates with the total personnel costs...

I won't say more about that

Better services are indeed when you don’t have to wait 6 weeks for an appointment as soon as you mention the word private...

...The contributions are rising..what if I have 3 more children? ...!

Well, you have to be able to afford children. A Hz4 recipient is advised to use contraception.

you almost share the amount 50:50 with the employer....

Nothing is shared there. The employer pays what he has to (whether according to the employment contract, collective agreement, or law) so that the employee does the work. Conversely, this means that all labor costs (i.e. gross salary + employer's share of social security contributions +, if applicable, capital-forming benefits and/or company pension scheme, job ticket, canteen subsidy, etc. etc.) have to be earned by the employee. Therefore, I consider the term employer's share to be misleading. The only good thing about it is that an increase in the amount automatically led to a (partial) wage increase. Back then, before the "employer's share" was frozen.

Therefore, as a sensible person, one should always keep an eye on the entire gross amount and consider all deductions in full.

And what good is it to me as a regular employee when I see the gross amount? No matter where I go, I will pay my xx percent in contributions, e.g., for the health insurance.