Mifare Classic IC info and block data cannot be read via iOS, This is because Mifare Classics do not conform to the NFC Forum specification for NFC, Therefore only NFC R/W chips made by NXP can communicate with Mifare Classic. The NFC R/W chip in iPhones isnt made by NXP and therefore can't communicate with Mifare Classics.
Writing to Mifare Classic on iOS is not possible for the reasons mentioned above.
iOS may not be able to communicate with Mifare Classics directly but it can interpret NDEF records written to them.
If a Mifare Classic has a compatible NDEF Record written to it (by way of another device), That record can be prompted to the user as usual. This means that iOS can recieve NDEF Messages from Mifare Classic just like any other NDEF Capable NFC Tag.
Within the iOS App "Shortcuts" there is the option to create automations.
Mifare Classic can be used as an NFC trigger for automations, this doesn't write anything to the Mifare Classic it just tells iOS what to do when it sees the UID of the tag you introduced to the field.
https://www.nxp.com/products/wireless-connectivity/nfc-hf/nfc-with-ios-13-:NFC_IOS_13#solutions
https://www.nxp.com/company/blog/ios-13-and-mifare-power-innovative-smart-city-use-cases:BL-IOS-13-AND-MIFARE-SMART-CITY-USE-CASES