Will leetcode DS & Algos make me a better programmer or is it firmly a skill for big tech interviewing?

• If you are able to get the interview at Google (or any big tech co), spend most of your time doing interview prep.
• If you are unable to land the interview, spend most of your time doing personal projects, or cultivating relationships with people who can eventually give you a referral.

Will leetcode DS & Algos make me a better programmer or is it firmly a skill for big tech interviewing?

It's very much the second. There are also many non-Big Tech companies that use DSA questions, but the overall point is that it's a parasitic activity meant entirely for interviewing.

I'm not sure whether to use my free time to work on a personal project or if I should use the time to take up a DS & Algos udemy course, Algoexpert, etc and just leetcode until I can apply for the big G.

Check out this discussion for insight into how you should spend your time.

... just leetcode until I can apply for the big G.

You can apply for the big G whenever. In fact, you should just apply now! A very common trap I see among software engineers is they optimize for problems that don't even exist yet. It's possible that your portfolio doesn't even qualify for Google at the moment. Wouldn't you much rather figure that out now instead of 6 months into the future with 250 hours wasted on Leetcode practice? You learn when you try stuff and fail, not when you're "preparing" in isolation. Check out this other excellent thread about interviewing.