Looking for Cdramas with strong/mature FL and healthy relationships

The Story of Ming Lan

I think a great drama for you to look into is "Meet Yourself." The female lead is mature, thoughtful, and well-written. She and the ML work very well together and are such green flags in terms of a realistic, healthy relationship in my opinion. 

I think Dream of Splendor has everything you asked for. one of my favourite dramas.

an ancient love song

Warning: it has a sad ending

FL is really strong and smart. She is really good at Archery as you can see if you watch the drama. ML is weak but he is smart and teaches FL stuff in later episodes that will be useful in early episodes. Their relationship isn't toxic at all and both of them love each other even though they do not kiss each other. The drama is in reverse timeline so when FL first meet ML he doesn't know her and vice versa. 

I'm not sure if my suggestions will fulfill your expectations, but I enjoy legally romance, sword snow stride, here we meet again, double love, and others.

She and Her Perfect Husband +1

Flight to You - FL is a headstrong pilot. ML is an experienced commercial pilot and a stickler for rules. So their miscommunications revolve around that. Otherwise he is caring.

The Rational Life 

I second so many others already mentioned here, but I'm currently watching You Are Desire and it is just wonderful. Strong leads and almost none of the tropes.