Things in your favor:
-You like what you do, and are good at it
-Your leader know this, as do others
-HR told you to let TLs handle coaching. (Yes this is actually a plus in my book.)
These are big positives.
Points you should re-examine:
-the existence of sub-par team members on your team means your leads don’t appreciate what you’ve done or do.
My read is that your store has a staffing shortage—your missing leads, team members, etc. And as your own SD referenced, the store was previously broken. The sad truth is that in certain situations leaders have to keep sucky people short-term in order to get the better people long-term. Sounds like this is happening with the people on your team. You can’t carry the team all the time, every day. (But push stills needs to get done everyday.).
-Leaders are cliquey, talk down to team-members, nepotism...
I’d be careful about letting your frustration with the situation create additional issues that might not actually be there. Every store will have clicks—that’s a given. And you will have leaders you don’t particularly care for. But that doesn’t mean there’s a conspiracy.
If you like what you do, stay positive, and do you. Stay close to your leader and help them. Don’t fix the mistakes by the other team member—if they suck, they’ll dig their own grave. If you like your job, don’t let the situation get you down. Stick it out, be positive, and it will get better.