The CC2531 adapter itself will never be automatically discovered. Instead, you need to first make sure meet the underlying requirements (such as making sure the CC2531 have the correct firmware and drivers installed) then you either need to install Home Assistant’s own ZHA integration (which does not have other dependencies so is easy to get started with) or use third-party Zigbee2MQTT application (which does have several external dependencies and then connect indirectly via the MQTT integration instead). Either will work but they have different pros and cons, so suggest reading up a little on both “ZHA” and “Zigbee2MQTT” before installing either (tip is that there are many YouTube videos which summerize those two):
So do you mean that have problems configuring it in Home Assistant’s own ZHA integration or are you planning on using it with the third-party Zigbee2MQTT application and connecting it via a MQTT broker?
Notes! First of all, note that regardless if using Home Assistant’s own ZHA integration or Zigbee2MQTT you need to first make sure that a CC2530/CC2531 Zigbee Coordinator adapter has the correct firmware, as many if not most CC2530/CC2531 are sold not sold with a Zigbee Coordinator firmware, (both the ZHA integration and Zigbee2MQTT are however at least compatible with the same Zigbee Coordinator firmware for them). Also note that you can not use both the ZHA integration and Zigbee2MQTT with the same Zigbee Coordinator adapter, (you could use both separately but then you will need to get a dedicated Zigbee Coordinator adapter for each of them).
Regarding CC253x limitations; note that CC2530/CC2531 is now very old obsolete hardware and unmaintained decapitated firmware so while you can use it to get started with it is to add just a few devices in order to test you are likely to quickly reach its limits soon if you start adding more then a few devices or you try to connect newer Zigbee 3.0 device more than basic features, so highly recommended that you buy and migrate to a newer adapter like example EFR32MG21 or CC2652 (CC2652P). See example: