My wireless headphones does not appear on my iPhone's Bluetooth devices list:(

I have a Sony MDR-1000X wireless noise canceling stereo headset (manufactured in 2016 I believe). I tried pairing it with my iPhone 12 mini, but it does not appear on the Bluetooth devices list. Could it be the difference of their Bluetooth specifications resulting in such issue? If not, does anyone have any idea resolving it? Thx