Switzerland narrowly approves plan for digital ID

Is that a fair comparison?

That depends. For me, yes.

If supporters of the digital ID say that they are not mandatory and that they are equivalent to physical national IDs, why can’t an Austrian teacher simply use their physical ID?

And how should I log in into Socrates with my physical ID? Like every time I want to access to make a photo of my physical ID and load it to Sokrates?

We are not talking about two services from different companies.

We are.
First of all there is nothing like “the government”. It is built on different institute which are working together.
Second of all WebUntis as well as Sokrates are not governmental, they are capitalistic companies contracted with the government.

I would really really encourage you to read into what the Austria-ID, EU-ID and the E-ID (Germany) actually is a what an IDP and SP is. Because you lack of the crucial misunderstanding what it is.