Hello @Y1qdefrsgfsgsr ,
Let me use the "another" IC as an example. Once the Reset signal is released, the IC starts with its boot which typically consists of a two parts.
It is Analog and Digital boot where all power supplies and digital cores are initialized. The XTAL gets started after these two boots are done. The "boot" time depends on the architecture of the NFC IC (functions, ROM size etc...).

About your second question.
If the IC is in (soft) hard power-down mode, only a minimum peripheries of the IC are power-up and running. This ensures a very small current consumption.
If the IC is in active mode (no RF but cliock is running), the current consumption might be a few mA depending on the used IC.
Please also note that MFRC523 is very old product (around 20 years old). So it very depends on what IC from another company are you using for comparison. If you compare 20 old years product with some current IC, I can imagine such differece.
BR
Tomas