We have a project with stationary Bluetooth clients (10 clients)
There is also one Bluetooth controller in the same area
What options do we have for using repeaters and extenders that we can deploy in a fully unattended way, meaning what can we deploy that will reliably not require a lot of visits to power cycle or to physically adjust repeaters or extenders?
Have you used something to boost Bluetooth? Is it reliable? Does it require tweaking? Ideally we want the good old set it an forget it by providing sufficient Bluetooth signal coverage.
There are no generic Bluetooth Low Energy repeaters or extenders available like there are for WiFi as the idea of communication is a bit different (WiFi has one access point communicating with a lot of devices in the same area using the same encryption and the Bluetooth LE has typically a lot of individual server-client connections in the same area which could all have different operational needs and encryption etc.)
Of course it is possible to build a custom made repeater just for your application but it naturally takes away the bandwidth from the other devices and then there is also a one more device to install and configure.
If there are a lot of devices in the same area, then the Bluetooth Mesh should be considered. That is not compatible with standard Bluetooth LE devices so all the devices should be Bluetooth Mesh devices then. But then the nodes can forward messages from the other nodes as it has a mesh network structure.
To make the practical operating distance as long as possible, it is good to check few things first before doing anything more complicated: make sure that you are using the highest transmit power available, there are optimized antenna arrangements (like the devices are not inside metal boxes or too near conductive materials using an unoptimized antennas), there are no disturbance sources nearby like Wifi, microwave ovens or other 2.4GHz devices and you might also consider using Bluetooth LE Coded PHY a.k.a. Bluetooth Long Range (that could bring twice or even four times the range).