One question I had , what has Pike done or going to do that justifies his birthday being a holiday in the 24th century? That's a pretty rare honor which would require something pretty impressive.
Pike was an extremely well regarded captain (DIS Choose Your Pain) in a crucial period of Federation expansion and solidification, many years before he suffered a horrific fate saving a group of cadets. Plus whatever events of significance he may be involved in during SNW's run. I suspect the accident, heroics, and gruesome injuries beyond the capabilities of Federation medicine made for a pretty big story, elevating Pike's fame in the eyes of civilians not already familiar with his very impressive service record. Making his birthday a holiday is a believable honor for someone now widely regarded as a hero who essentially made the ultimate sacrifice, but is technically still around to appreciate the gesture.
Boimler is prone to exaggerating and has strange perspectives. It could be some obscure holiday on a planet he saved, or a Starfleet tradition to commemorate just on ships named Enterprise. Or there's another major holiday which coincides with Pike's birthday.
He reacted as if it was an actual Federation holiday, which would be stronger evidence if he wasn't already terrified he'd altered time.