### What this PR does / why we need it?
[CI] Update doctest from 0.9.1 to 0.13.0, and copy doc test workflow to
nightly CI for better monitor.
### Does this PR introduce _any_ user-facing change?
### How was this patch tested?
- vLLM version: v0.14.1
- vLLM main:
dc917cceb8
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Signed-off-by: menogrey <1299267905@qq.com>