I use the FT231X all the time in both bus-powered and self-powered applications, with the circuits recommended in the data sheet as you show. Never had an issue with one not enumerating on the bus, but I’ve never used USB-C connectors, either.
Running the LEDs to +5V is definitely not a good idea, but abs max for VCCIO is 4V, and you have probably not exceeded that, so as Joseph says probably no damage. Could be driving the chip crazy, though, so I’d pull the LEDs or their resistors and see if it works then.
Random comments on your design:
- Your use of copper floods for ground connections is sub-optimal in terms of inductance and common-mode noise. Much better to use a 4-layer board and get grounds to things like decoupling caps with vias to an inner plane. But probably not the reason your device is not enumerating.
- I don’t see the point of a fuse in this device.
- AC coupling DTR is a weird thing to do.