Yes, the Ti Birdy is factory equipped quit a 52-36 compact crankset and after upgrade has a 9-32 11s 3T/Ethirtheen cassette.

But with the 9-32t cassette I never need the smaller 36t chainring and have been considering to remove all that almost useless double chainring stuff (it was mounted because the original cassette was a stupid 11-28t with a too short range).

If you want a double with a front derailleur, you not only need to add a second chainring, but also to replace the factory installed 52t chainring which is not made to switch chainrings. The usual combinations that work with all front derailleur are 50-34, 52-36 and 53-39. To have best performances, you should take a set of chainrings from one single manufacturer because chainrings are optimized to work together.
You need BCD 130mm chainrings.
I would take a Ultegra front derailleur or a cheaper 105 and you need a shifter for instance a Shimano SL-RS700 left (for the front derailleur).