Multiple bluetooth LED to one controller

I have a project in mind where I want to attach shelves to the wall but have each triangle have a lit edge. I also want to make is as clean as possible with no wires showing BUT I also want control of each triangle and be able to group them together. For example if I wanted to turn all of em on with a simple button push but also be able to change one of the colors separately.

I was hoping to do a battery pack to a bluetooth controller to LED strip in EACH triangle, and then have all the controllers connect to a single receiver and then connect THAT to a simply programmed app on my phone.

Is something like this possible? And if so what would I need for that and if I can do that with arduino.

Bluetooth is a communication between one transmitter and one receiver, not several.

It is possible. And you can do that with Arduino. There are different ways to do it and each of them will have its own difficulties.

The one you mentioned: 1 battery and 1 controller for each triangle is the hardest way IMHO.

WS2812 LED strips can be combined together to make one strip. If you choose this path, you'll need only one controller. You can choose if all of the LEDs will be one line (one pin controls all of the LEDs), if each triangle will be a line (you'll need 9 pins), if each row or column of shelves will be a line (3 pins), etc... You'll have to map them on the sketch to make the effects you want them to do.

A wall adapter with enough power would be needed and probably different points of connection depending on how far the strips are from each other.

maybe worth looking at the ESP-NOW communications protocol

Wires will be needed, But what are your ideas for hiding them?

Note that Arduinos come in many form factors with many different capabilities, so it depends on what sort of Arduino you want to use.