It could just be quad tendonitis, a little inflammation maybe some tightness or even shortening of your quad tendon.
Then when you get into your tight bench setup, it’s a big stretch on the inflamed tissue, that you hold for awhile so you really feel it.
The easiest way to deal with tendonitis is high rep moves against band tension, so you can get full extension/lockout to train/rehab the area around your knee joint. I like leg extensions with a band rigged up on the machine. Stan Effecting used Leg Press vs bands to fix his quads. I’m not sure what equipment you guys have in the gym, or what’s convenient for you.
I guess maybe you could bench with your feet flat, maybe even with your feet in front of your knees for a little while as this heals up. Maybe think about a controlled descent and smooth reversal out of the bottom of your squats for awhile. Like limit the bouncy, tendon action, stretch reflex to give your quad tendons a break.