Cross-Talk/Interference between UART Lines on a PCB
4x spacing over a ground plane should be no problem.
I normally use a spacing of three times the trace width for normal signal traces.
Especially for UART signals that are relatively low speed there will not be an issue as most UARTS have noise rejection logic where they sample the signal three times so any coupling would be rejected anyway.
Clock and reset signals to registers are the most sensitive as any transient can permanently alter the sate of a register.