So a couple things.
Rasberries, blackberries, etc are biennial fruiters on a single cane.
Last years new canes will fruit this year and die off after fruiting. Probably only half or so of those canes are actually alive (coming out of winter, they'll fruit this year). New canes will come up from below and those canes won't fruit this year. They'll be the fruiting canes for next year. Once a cane has fruited, that's that and it dies off.
First maintenance step is to remove the dead canes from last year. They ain't doing shit. Clip them out at the base and mulch them.
Second step is more editorial, but I highly recommend this. You don't need to allow all of this years canes to grow/ go into fruiting. These put out so many canes that it can actually get in the way of accessing the fruit/ putting out quality fruit. I would recommend picking and choosing which of the fruiting canes you want to keep for this year. Make the decision based on how easily the cane will be to access for harvest (you don't want a crap ton of fruit in a place that's a PITA to get to)/ the health or size of the cane. Reducing the number of canes will allow the remaining canes to produce larger clusters of healthier fruit. I'd cut out almost half or so of the canes that will be fruiting this year, most just to improve access.
Looking at that patch, I would estimate maybe 1-2 hrs or less of actual maintenance required. Very small price to pay for fruit.