The bug
Before 1.14, beacon beams stopped at the build limit (256 in my example) but in this screenshot, they don't.
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They will instead go as far as the player could render the beacon. I am very sure the developers manually rewrote the beacon beam to render like this, so this is very likely intended. It looks way less ugly too.
Hi there!
I can confirm in 1.16.1 and 20w29a.
Beacon beam stopping at the build hight limit was intended per MC-67975.
Can confirm in 21w06a.
Can confirm in 21w07a.
I activated a beacon in Y=-62 and the light goes from -63 to 960

I noticed that beacon beams are glitched at the height of 1100
Can confirm in 1.17.1

I tested this in several worlds, placing the beacon source at different heights, and noticed that the height of the beam is fixed and it is 1021 blocks

Can confirm in 1.21-pre2
Probably WAI.