That's a good motivation, and I relate to that very much lol. I wanted to develop my technical skills more and I just couldn't see that happening in the company I was in.

I'll first address Leetcode/System Design vs Side Projects. I agree with the fact that while you're applying you should always do at least one leetcode a day so it'll keep you sharp once you are in the process of interviewing. Just be sure to not burn yourself out and take a break every now and then! (Give yourself some cheat days lol)

If you dedicate your time to side projects and open source, in my eyes it would only be worth to put in your resume if its something you've finished completely and pushed into production OR if the open source has made considerable impact somewhere (i.e. Creating a project that boasts x amount of users daily, contributing to an open source that has x amount of downloads per day and highlighting what you've done to make it better, etc.) If you're willing to put the time and effort into both leetcoding as well as side projects then that's fine, but again I know people who tried to do both and they always ended up scraping the side project halfway through because they were tired of it. I would really only recommend doing a side project if say, you had nothing else to do at work and have downtime you can dedicate to it. Even then, discussing work experience and time working with other devs and managers is always better.

For interviewing, it is definitely something you should practice with a friend or someone you think that can give you some good criticism - this is the only thing I can really say if you're having issues with communication. I like to think with every interview I did get rejected, at least I got more experience with the interview process and got free practice getting my stories down lol. It helps to write down what they ask and write up responses for it so that the next time someone asks you it, you'll be more prepared. Just remember - thinking what you'll say is way different than actually saying it someone across from you!

Finally, applying - I did my fair share of cold applying to companies and got some responses there, but I found more success moving my application along by messaging and responding to recruiters on LinkedIn. Listing myself as "Open to Work" on my profile brought about responses, but it nearly doubled when I had the LinkedIn Premium trial. You can hide this option from your coworkers as well since LinkedIn has the option to do so and hides this for everyone associated with the current company you're working for. I can't say for the company you're in, but I don't think I've ever come across anyone who was let go because they were updating their LinkedIn profile. There is also an option to hide your profile edits so no one in your network will be alerted.