The iPhone 12 mini has an A14 and the iPhone 14 an A15 processor. Geekbench single core performance is 7% better in the newer one. I doubt you're "feeling" the difference in speed between these two phones.
The battery life in the 12 mini was not considered good from the start, so it's understandable, that after two years the battery is in not so good shape anymore.
Only in multi core. Single core performance is up 18%. I once read you need at least 20% higher speed to feel an improvement. Perhaps the 120 Hz display is a much higher factor in the perceived performance in your new phone.
