I found a video that goes over this in detail
The point he makes in the video is that, regardless of era or universe, we see phasers emit in both pulses and streams.
Most people expect phasers to look like this
The list of places they appear like this is... well, it's long
- NCC-0514 (USS Kelvin)
- NCC-74656 (USS Voyager)
There are instances in pre-Discovery canon of pulse firing. The most notable is Star Trek II, when Khan attacks the Enterprise
So pulses are not necessarily non-canon.
So why the switch? A couple of reasons
In-universe, phaser technology has had to advance due to the Klingon war. We saw this in the Kelvin universe, where they went the other way (beams on the Kelvin, to pulses on the Enterprise, likely to counter the Nero, which had that multi-torpedo launcher). It's likely the Discovery got a refit at the end of Season 1.
Out of universe, it would be silly to have the original NCC-1701 firing beams (to better mesh with the phasers seen in TOS) while the supposedly more advanced Discovery was still firing pulses. I should note, though, there were still a lot of pulse phasers in the final fight of Season 2