The OP is probably from one of the EU countries where you see those things only in museums.

(And we actually have problems when visiting USA because some of our banks issue credit card with numbers printed instead of embossed.)

You can certainly get a notification at the time the issuer finds out about the charge. Typically that's instantly, but on an old imprinter machine it may be delayed. You still find out as soon possible.

"online authorisation" means the POS terminal authorizes the transaction with the issuer. EMV is a complicated protocol and that may not always happen for whatever reason. One example is the terminal has no internet connection but the terminal may also be programmed to not do it in certain cases for various reasons (eg. speed up checkout).

In these cases your issuer will learn about these transactions when the nightly batch job finishes. I don't think you want to get an SMS at that time.

Even if the authorisation is successful the final transaction may not happen, may happen at a different time or may happen over a different transaction amount.

Honestly I have no idea why I got downvoted.

Ok, that can be different elsewhere but my experience with German cards in some European countries is that contactless payments are almost always online authorized even if no cardholder verification is required.