Direct mount rear derailleur

I’m upgrading an old MTB for commuting, it had a 5 speed on the back but I’m going to be putting on a new 26" rear wheel with a 7 speed cassette because the freewheel axle wobbles, makes noises and is clearly done. The rear derailleur needs replacing because it doesn’t changing gears properly and it jumps out of some gears. So, I got a new chain, front & rear derailleur and I’m just waiting on the 7 speed gear selectors, all cheap parts but all I need.

The only problem is whether I got the right rear derailleur for the bike. There is hanger mount and direct mount, my old derailleur seems to be a kind of hanger mount but I read direct mount is better so I ordered that.

Can you tell me if the new derailleur will work with the new 7 speed cassette, I know it says 6 speed but it has enough travel to go from the spokes to the smallest gear. The way is sits on the bike is pretty far back compared to what was there before.