There are memory card readers and SIM card readers. Can a SIM card reader be used to access mobile data? As in, use 4G/mobile broadband?
Or any other way to access the SIM's mobile data from the laptop, which does not support the insertion of a SIM to the laptop itself (without using the phone's hotspot, because that will drain phone's battery faster). Laptop doesn't support eSIM either.
A SIM card reader gets information from the SIM card. Nothing more and nothing less. Just having that information does not mean you can use "mobile data".
The question becomes what do you intend to do with that information? How do you intend to exchange that information with someone who can allow you to use mobile data?
The SIM card does not contain a mobile phone radio, it just contains the information used by a mobile phone radio to connect to a mobile phone network.
The frequencies used by mobile networks are very different from those used by Wifi or Bluetooth, and the encoding of data and power levels used are also very different. None of the "normal" radios present in a PC can communicate with cellphone towers as they lack the radios and protocols necessary.
A SIM Card Reader is only a small part of the hardware necessary to allow a computer to talk to cellphone towers and so "use mobile data"
You can get LTE adapters (or laptops that already contain LTE modules) that contain all the radio electronics necessary to talk to a cellphone tower, but normally these also contain a SIM card slot so your SIM Card Reader is completely redundant and useless in this case.
So no, a SIM card reader alone is not enough.
The only way to access a SIM card is via a SIM card reader. You can use the one already build e.g. into your phone (use an USB cable if you don't want to access the WLAN connection through your phone) or you can pick one up for a few bucks. Make sure to get the appropriate software to read the SIM card as well (depending on the data you want to read from the card).
Update No, you can not connect to the internet via a SIM card reader because a SIM card reader has no way to access the mobile network (G4, G5, etc.). You'll need a "mobile USB modem (for SIM cards)", a "mobile WiFi Hotspot"/"mobile router", there are several options available on Amazon, eBay, etc. Alternatively, you can connect your smartphone via a USB cable.
