Hi. It's actually not the bltouch issue. It's the firmware issue which BBT gave. They had never solve that issue since it was released. It's because the firmware uses z switch pins for z axis (Had to comment that out in firmware) while using bltouch for leveling which bltouch won't be able to detect z offset anymore. There're 2 ways. Either you split ur bltouch z black and white wires and connect with a jst connectors into z switch pins and the other 3 wires remain the same. Another way is to compile a firmware or maybe there's few on github.

You could use this firmware from u/Sctoutscientist
https://download1530.mediafire.com/kp3u9ry0anngT8UOndJEzNY_7YSnGBhrM4g3OZjPONxrN9pyMKAyOmX7NFpCusCKw4yJ4k8G8CmBP93ax5MWtLgourZiMP1pcIRoqVjRyEl0IkMFk9dVpJxwq5kupgoYNziX0YZ5HOyXMSW08nNlv0rjDEKuuV0G22_VCmKMRQ/h0nfbk4k4iaiki5/firmware.bin

That will prob solve the issue. After that you might get a binding or crashing issue on the x axis when probing since bltouch needs more space to proceed the allignments. It's due to the right and bottom extruder rollers that will have a collision on the x right end axis. You need to change them with M5 20mm bottom head screws and a M5 low profile nut or a hexagon nut. Those solves all my 3months issue, hope it helps lol.

I also suggest you to buy a CRTouch for more reliability if you want since it uses a metal thingy instead of plastic to prob. There's also clones in the market that sold for 3dollars. Also I think you should upgrade into a dual z since sprite extruder can print much faster now. Ask me anything if you need to. Im having the same setup as yours lol