I think it's interesting that the Shenzhou was still outfitted with phase-cannons and not lasers.
As far as we can tell, Starfleet starships were never armed with lasers.
TOS "A Private Little War" makes reference to "old style hand lasers", and apparently the three-barreled phasers seen in the early TOS episodes featured at least one laser barrel which the excited Tyler there mentions as having failed to cut through Talosian doors.
(That other Tyler, from DSC, might well have had a laser barrel in his three-barrel tool of trade, too, but the only time he explicitly used a laser was when it was mounted on the manipulator of his workbee. Technically, this would be a spacecraft-mounted laser, but it didn't appear to be a weapon. Also interestingly, it is the only laser in the history of Star Trek that does the thing no laser should ever do, that is, glow in vacuum!)
Nobody ever specifies what kind of a beam weapon (if any) Pike's starship had in "The Cage". Also, nobody tells us what kind of a beam weapon was ultimately used to blow the Talosian door (and hilltop!) to smithereens. But later Trek artists have taken the double-bubble structure of that pedestal projector and applied it as their symbol for the shipboard phaser emitter in the Master Systems Display artwork; also, the colorful beam effect of that projector would thereafter be used for the beam of Kirk's explicit phaser rifle. So presumably the pedestal device was a phaser gun or a phaser drill. And presumably Pike's ship also had phaser armament, since ships before and after that one did - but there's no other data on Pike's ship-mounted death rays on that fateful day, so we might theoretically ponder doing hypothetical speculating...
From its blend of the NX and Starship-class, it's at least thirty years old by the time of the first episode of DSC. So, maybe the powergrid can't support anything newer than twenty years old or so. But, on the other hand, it's clearly been refitted with the newest warp-nacelles as they look almost TMP-era.
Or then the newest news is the boxes on every other ship seen, and they in turn will next be replaced by the art deco things first spotted in ST:TMP. The Shenzhou nacelles might fall in between the ENT era cylinders and the DSC era boxes; perhaps their odd, even alien shape is due to Starfleet adopting some off-Earth technologies in the aftermath of the formation of the Federation, and then giving those up in disgust when it turned out domestic was superior?
Timo Saloniemi