New lease and registration/transferring plates

I tried to search for these specific queries in the forum, but couldn’t find anything directly related.

I just traded in my old car, signed a new lease on Friday. They transferred plates and taped a temporary registration to the windshield.

On the old car, there was a month left before the registration expired. Am I liable for that, having signed over the title to the leasing company? I just got another reminder from the DMV, probably auto-generated, to renew registration.

With the new car, would I be right to assume the dealer also got my new 2-year registration? The salesman said it should come in the mail in 30 days, but when I called the finance manager to clear up the registration issue on the old car, he seemed pre-occupied and reiterated going to the DMV to file the proper paperwork if I transferred plates.

Forgive if repeat. Brain fog from busy week.

Lastly, for anyone in NY - when you upgraded your license to Enhanced, did it give you a new ID#, or 'doc #?" I tried to clear this up by signing up for the DMV app, where you can check status, but it’s saying my info is wrong and the only thing I can think of is having gone in person to upgrade 2 weeks ago.

Your registration stays with the plates. You’ll need to go online on the NYS DMV website and renew for 2 years.

When the new sticker comes in the mail, just tape it onto the windshield with scotch tape. Just in case if you/dealer/title company paid double, you’ll be able to return the unused sticker for a refund.

Many thanks! Very helpful!