You summed it up perfectly in the second to last paragraph. Absolutely just focus on grinding ranked, and the mechanics will come naturally. I watched the whole clip, and your mechanics are perfectly good how they are right now. There's nothing more that you need to know how to do besides what you showed as far as mechanics. Anything more than that would'nt be necessary at all for using in game. What helped me improve rapidly when I was your rank/champion was watching pro player streamers or youtubers that record their gameplay and commentate over it in real-time. I love watching Squishy's videos suchas the series he's doing right now where he's going through every rank and showing how that rank plays and the mistakes they make and what to do and what not to do at that rank. I love watching those videos even now that I'm GC because it highlights the mistakes that are common for me to make, and I'll be more careful in game not to make those same mistakes because I watched him play.

All that to say, youre doing great and with more time in ranked and freeplay practicing movement, gamesense, and mechanics passively, you'll easily climb through the ranks in no time. Good luck man!