"In this sort of predicament, always ask yourself: How did we learn
the meaning of this word ("good", for instance)? From what sort of
examples? In what language-games? Then it will be easier for you to
see that the word must have a family of meanings."
-Wittgenstein, in Philosophical Investigations
Investigating and clarifying definitions is an essential step toward having a productive discussion, by making sure the parties involved are using the same terms for the same things, and investigating internal contradictions and inferences. But that is just one step. Crucially, context is important. And science and society and even philosophy change, so our understanding of some terms must shift.
Consciousness is a good example, because our understanding of mechanisms is jumping forward all the time due to better ways to look at and act on the brain, plus insights from computational work like image processing, and natural language processing and approximation. But there are huge gaps, like minimal understanding of how our memory works, a remarkable lacuna in progress, as I understand it. Clarifying definitions can only pen-in edges for the task of understanding consciousness, they can't do the unfinished work of learning how we do what we do.
Wittgenstein saw philosophy as primarily a kind of 'linguistic therapy' in the way you describe. He understood it as 'shewing the fly out of the bottle', of our contradictory uses of words:
“The confusions which occupy us arise when language is like an engine
idling, not when it is doing work.”
-Wittgenstein, in Philosophical Investigations
So for him, the work of understanding what Chalmers calls 'the easy problems of consciousness' is for science. And the Hard Problem of consciousness is just a failure to understand we can't have a Private Language, that is it results from linguistic confusion.
Living well, meaningfully, authentically, virtuously, or by other standards, points to how there is a side of philosophy about a personal practice, of self-knowledge and skillfulness in how to be, where philosophy can be more of a toolbox we bring to bear on our own personal problems. And that is the thing about Wittgenstein's austere interpretation of the job of philosophy: you don't just clarify a definition forever, problem solved. Ambiguity, confusion, speaking at cross purposes, implied context or subtext not all parties are aware of, and a million other issues can reoccur in literally every conversation.
So we aim to develop skills. Like identifying formal and informal fallacies, helps conceptualise identify and avoid, things that come up in debate and discussion that tend to mislead or derail conversations, that may indicate bad faith in one party towards honest pursuasiin or sincere commitment to finding an answer or agreement or determining what is true.
Philosophy aims to help us think clearly and consistently, to have priduxtive discussions, and so to live well as individuals, and together. That must require an active practice, honed skills. It is an unfashionable term in philosophy, but in this answer I relate these skills to wisdom: Wisdom and John Vervaeke's awakening from the meaning crises? Clear definitions for a given discussion, is surely the beginning of wisdom; but by no means the end of it.