Yes, as said before RD4 and RD45 is almost identical. The RD4 has "TA/PTY" button, the RD45 has only "PTY", but the fact that you have BT_RADIO showing on your phone confirms it's an RD45 radio.
The other thing you need is the screen on the last picture. It's called the multifunction display, EMF_C type to be exact. The question if it's EMF_C or EMF_C1. For the BT to work you need the EMF_C1 version. There is a sticker on the back of the screen which tells you everything about it. There's also a SW Version line, and that has to be at least V72.2 I believe for the BT to work. If not, then you need to replace the screen. You can buy them second hand from eBay, some scrapyards might have it too.
If you have a correct screen, then you'll need somebody with Diagbox to enable the settings in the displays menu for the options to show.