What Control Center customization can and cannot change
You can freely add, remove, and reorder individual controls, and on some iPhone models resize a few of them, but you cannot change the overall Control Center layout itself or move it to a different swipe gesture.
A few genuinely useful additions people forget
Screen Recording, Low Power Mode, Text Size, and Magnifier are all available to add but are not in Control Center by default on most setups, despite being ones people commonly wish they had one swipe away.
Frequently Asked Questions
Will my customization carry over if I switch to a new iPhone?
If you restore from an iCloud or iTunes/Finder backup, your Control Center layout typically comes over with the rest of your settings.
Can I set different Control Centers for different apps or situations?
No, iOS only supports one Control Center configuration system-wide -- it does not change based on which app is open or your location.