I have two options:

Leaving my current role to join a big Bank as a senior engineer

Or

Staying at my current company and get promoted to Tech lead(my current company has been having some major layoffs

What do I do?

whichever pays more.

Work to learn or work for money is okay to do either, and best to do both.

Likely, you know your current gig inside and out. You may have plateaued with what you can learn there; and moving usually means more money

I'd move.

Context: 7 months into a giant company coming off of 10 years of start ups. I'm learning lots of leadership style stuff, not so much the tech.

Look for a third option

Go for the Bank job. Don't stick to any company for more than two years. If your current employer is having layoffs, it's highly likely you're never getting that raise or promotion in recent times.

I faced the same situation, after massive layoffs, asked my company for a raise, since the workload increased exponentially. Waited three months with no advancement, and tomorrow I'm joining a new company. Granted it's another tech company, but they are paying me more than what I had asked my current employer for.