So I finally got the matching bleeding kit and got around to bleeding the brakes. Rear brake went completely smooth - was done in 5 minutes or so.
Front brake however - it seems like the brifter is leaking air somewhere, when I pull on a brake lever, there's a sloshing noise, similar to sound you get when you are pushing in a water bottle. The sound is coming from the top of brifter, both the oil and air screws are fully tightened. Any ideas what could be the issue? Don't have a video at the moment, apologies.