How quickly are plants able to sense changes in light intensity?
The delay for UVR8 photoactivation seems to be in the range of picoseconds depending on the wavelength:

Global analysis in terms of a model of parallel decaying
components indicated four lifetimes of 14.7 ps, 370 ps, 1.9 ns,
and 5.9 ns.



The photodynamics of the Trp ensemble in UVR8 can be summarized as
illustrated in Figure 5B. We observe excited state decay in the
few-hundred- picoseconds to nanoseconds time domain to the triplet
intermediate U460.

<img src="https://i.stack.imgur.com/Sz4zK.png" alt="Tentative photocycle of UVR8
photoactivation as observed in vitro." />
For a better understanding of photoactivation mechanism times, you can read the following article:
Proton-Coupled Electron Transfer Constitutes the Photoactivation Mechanism of the Plant Photoreceptor UVR8
Journal of the American Chemical Society 137(25) · May 2015