Grinding noise on startup 2010 Honda Fit

2010 Honda Fit, Manual Transmission. 84,000 miles

On cold starts (the weather is also cold here if that is important) there’s this prolonged noise after the noise of the engine turning over that’s like a grinding noise.

It typically only happens the first start and not again after that. Although it has happened twice in a row, after starting – turning the engine off- then starting again immediately after.

Everything shifts smoothly with the transmission, I’m hoping, if anything it’s a starter issue and not something more serious. I’m a bit of a novice but I do know the starter turns the flywheel, and the clutch also interacts with the flywheel, but shouldn’t be even touching the flywheel while the clutch pedal is depressed for start?

If any questions need to be answered to get a better idea feel free to ask. Thanks.

I actually found a video that makes the same noise as my car https://www.youtube.com/watch?v=htZg6EEtyfk
at 0:30