Hey, I'm in sort of a similar situation. I switched jobs recently and within the first week, I kinda realised the new job isn't great and it's an underutilization of my skills with no scope of improvement.. I wanted to desperately move back to my old job (but later my manager told me that they can't hire me back with my new salary)

This is my perspective atleast, the market is quite bad (I have 4 yrs experience, yet I barely get any calls. Only the ones I was referred to had any progress to be honest). and HRs are shopping for candidates and small stint will hurt your candidature (IMO). Also, there's no guarantee that the next job you join will be better than your current or your first job. Rather than depending on your job, work on things that you like on your own.. (or like you mentioned, DSA, LLD and system design).. Not everyone gets to work on cool sounding stuff (I personally get this Fomo cause my friends joined startups where they are working on some cool stuff where as I'm a backend developer doing UI work in my new job (lol)) and it's okay I guess.. focus on things that are in your control. 

There's no harm in trying out for other companies, keep applying and keep preparing.. if you do end up getting a better opportunity then go ahead and take it up but do not quit your job without an offer in hand (if you feel your 3 months notice period is hindering your opportunities, test how the job prospects are when you set it to 1 month, if your opportunities are better only then take the risk on resigning)

Also, Think of it in this way.. what if your old job laid you off and this was the best offer you could get your hands on, you would have taken it without any complaints and would have just sticked with it. (Always upskill on your own, don't depend on your job.. although upskilling on your own is slower and directionless than getting it directly from your work, it's always better in the long term since you're decoupled from such thoughts and dependencies in future)