> obvious that it's not going to use the popcnt opcode instruction ... I'd guess totally impossible in Java

I don't understand why you would guess at what Java can do when you can find out for certain?

    public class Test {
      
      private static int bitCount(int a) {
        return Integer.bitCount(a);
      }
      
      public static void main(String[] args) {
        while (true) {
          bitCount(14);
        }
      }
      
    }

Compiles bitCount to

    0x000000011e637980: sub    rsp,0x18
    0x000000011e637987: mov    QWORD PTR [rsp+0x10],rbp  ;*synchronization entry
                                                  ; - Test::bitCount@-1 (line 4)

    0x000000011e63798c: popcnt eax,esi            ;*invokestatic bitCount
                                                  ; - Test::bitCount@1 (line 4)

    0x000000011e637990: add    rsp,0x10
    0x000000011e637994: pop    rbp
    0x000000011e637995: test   DWORD PTR [rip+0xfffffffff10ed665],eax        # 0x000000010f725000
                                                  ;   {poll_return}
    0x000000011e63799b: ret 

There's your popcnt instruction. No need to guess.