Does not appear to be crimped to me. Mostly it is military ammo that has crimped primers. My H&K 91 and 93 Rifles both crimp the primer in when the cartridge is being fired (along with striations longitudinally on the cases to assist extraction). Again, no I don't think it is crimped.
Hmm. Can you shoot an uncrimped commercial 308 Win or 223 Rem round in your H&Ks and report back if it comes out crimped?
I've fired a fair number of H&K rifles. I'm familiar with the fluted extracted cases, but I've never heard that the rifle is crimping the primer.
I assume those primers were crimped before they were fired.
To the OP:
I don't use Hornady brass, but that looks more like more like a quirk of their process rather than a crimped primer.
I have seen 300 Win Mag crimped primers, but never 7mm Rem Mag. There is 300 Win Mag being used by military snipers and MIL-SPEC requires the crimp.
You can find just about anything in range pickup brass. "Civilian" 223 brass on commercial head stamps with crimps, etc. Ammo companies will make ammo runs based on the terms of supplier contracts, so anything is possible.
I would first see if you can easily re-prime it before making an investment in more gear. If you are nervous about trying to get a new primer in a tight pocket, pick a spent primer from a known un-crimped round and see if it goes in easily first, then run the case through the process again and see if it takes a live one.
If you invest in a universal de-priming die, you will not regret it. I use the RCBS one. It has a spring driving the de-capping pin which gives a little extra push to kick the primers out with some force. This is designed primarily for progressive press users, but I use it on all crimped primers in a separate step from my sizing die. Sometime a primer does not want to pop free, making you think the stem on your sizing die is adjusted wrong. Then you lower the stem and bend it on the next round. Not cool.
The universal de-capping die prevents this and pays for itself in saved downtime getting bent de-capping rods replaced. The die is also very handy when you "oops" and get a primer upside down or mashed in there sideways. The die doesn't touch the outside of the case so you don't have to re-lube and possibly re-trim as you would running it through your sizing die.
Most of us started out just reaming out primer swages with a de-burring tool. The motorized case prep all-in-one machines also ream the crimp out. It is not a big deal, but it removes brass and I avoid it. You can find an RCBS press mounted pocket swager pretty cheap used. That's what I use now. I am budgeting for the $100 to get the bench mounted unit.
The RCBS youtube channel has good videos on dealing with crimped primers.
Handloading can become a real passion, be safe and have fun with it!