What could be causing my bike's brakes to feel spongy and less responsive?

I've been experiencing a spongy feel in my brake levers lately, and the braking performance has noticeably decreased. My bike is a Shimano-equipped road bike, and I've recently replaced the brake pads and bled the system, thinking that might resolve the issue. However, the problem persists. I’ve checked the brake cables for fraying and ensured they are properly seated in the calipers. My first thought was that there might still be air in the lines, but I’m unsure how to confirm that or if there are other potential causes. Could it be related to the brake lever itself, or is there something specific I should look for in the calipers? Any tips on troubleshooting this issue would be greatly appreciated, especially if you’ve encountered similar problems.