What is the maximum number of BLE connections that can be achieved with the BT85x or BT860?

The Cypress CYW20704 A2 chipset, which the BT85x and the BT860 is based on, theoretically supports up to 127 Bluetooth LE connections. However, because the BT860 is an HCI module it is dependent on the Bluetooth stack running on the host therefore, the number of connections will depend on what the host CPU and memory capacity can support.

Additionally, as the number of connections increases, the throughput per each connection will decrease and the processing and memory requirements will increase, which can lead to increased latency. So while 127 is the theoretical limit the actual limit in practical use case would be less than that.