Cool, Old Curmudgeon...
During the first few weeks after quitting smoking and switching to vaping:
-you will get a runny nose, especially after a good round of vaping while exhaling through the nose. It goes away after a few months.
-I never had a problem with phlegm, although I smoked for 35 years before quitting and switching to vaping. I had more of a problem with phlegm while I smoked and it went away after I quit smoking.
-I know people who have smoked since WW2 (one served under Patton in artillery) and quit smoking recently. The one who served under Patton had problems with phlegm and it never stopped after he quit smoking. It's just a symptom of more serious lung damage than I have. It's was more of a nuisance to this person than a health problem.
You may have to live with the phlegm, but the runny nose will probably go away.