epic

Hate to be that guy, but even if they had MG42s mounted on light vehicles that aren't a motorcycle with a buddy seat, and those were common enough to be in a random prison camp, they wouldn't be using them in a forest. Great way to lose the vehicle and then get fucked every which way for that.
They'd just send a platoon or two of regular grunts each armed with an MP40 because having more eyes and legs is more important than speed and firepower. The escapees would be likely much worse fed and have worse fitness overall, and know the area about as bad as the grunts, except a few of the grunts might've been on leave or AWOL without anyone outranking them knowing and they'd probably be briefed at least a little before being sent on a search.
Oh, and there'd be dogs.
And the grunt on the tower would probably have a Kar98 which definitely doesn't have a full auto mode.
And the sadly lone survivor would be very unwise to throw out the free Luger he got because there can be wildlife and it's better to risk recapture than being eaten alive by a bear because bears are cunts who don't even have the manners to kill you first like wolves do.

Kudos for not including a minefield. It's more realistic to not have one as that'd be excessive but still I was expecting one of the guys to get like 2/5 of his body blown off and lie there screaming in agony when they got to the entanglements. War sucks.