Usually no sign before failure except probably on mechanical side like bearing

The battery warning light is indicator that the battery is not charging or low voltage. So, either battery or alternator is bad. Mine nothing at all and suddenly engine died. I can't recall if there is indicator long enough on display. I think it is not total failure. After a while due to chemical reaction, I can start the car again and drove car home 1km away.

The multimeter measurement is not that reliable measure. If the battery cannot hold charge that good, after driving your battery voltage would probably show good voltage but store less power. Multimeter is just measurement of voltage but not how much power has been stored. Voltage level is quite meaningless for this purpose.

Voltage low cam be either battery or alternator. Anyway, who would check battery on regular basis like every morning before go to work

In your case the alternator is not giving out enough current to charge the battery. In my case, I'd say the electronic components in the alternator just failed with no sign. The car started as usual with no difficulty at all.

This is on troubleshooting stage already after failure suspicion, should there be sign of it. For me, I'd just go to nearby workshop to check because they usually do not charge for simple check like this

Agree. This is wear part