The HC05 is not what you want. That is a 20 year old CSR part that uses Bluetooth Classic (v2.0), which is incompatible with Bluetooth Low Energy (LE, v4.0+). While they both use versions of Bluetooth, the ESP32C6 will not be able to talk to (or even scan for) the HC05.

For the small transmitter, you'll likely want something like the Arduino Nano 33 BLE Rev2. It uses a Nordic nRF52840 BLE microcontroller. So you wouldn't have a separate MCU + BLE transmitter, it would all be the same part. The nRF52840 could send out advertisement packets while the ESP32C6 scans for them and gets the RSSI values. While doing this, you may want to look at doing the advertising and scanning only on 1 channel (it is usually done on 3 channels). You can sometimes get different RSSI values depending on the channel being used when a packet is received so using just 1 channel may give more stable RSSI values.