How much trig do I actually need for fabrication work?

Shop fabricator here, about twelve years in. Short version: yes the math comes up, but way less often than the course outline makes it sound, and it's never the scary version from high school. Ninety percent of what I actually use is right triangles. You know one angle and one side, or two sides, and you find the missing piece. That's it. Sine, cosine, tangent, three functions, and honestly if you can remember which is which you're ahead of half the guys I've worked with.

Where it actually shows up for me: laying out a miter on tube or pipe, figuring the rise and run on a staircase rail or a handrail section, working out setback on an odd angle bend, and calculating rolling offsets when you get into pipe fitting. Those rolling offsets are the one place the math gets genuinely useful and genuinely annoying. But even there, guys mostly plug numbers into a pipe fitter's reference book or a phone app once they're out of school. The school teaches you the long way so you understand what the app is doing. That's not a bad thing, it just means you don't need to memorize it forever.

Your instinct about the square and tape is right for a lot of flat work. A framing square plus the 3-4-5 rule covers checking square on assemblies all day long. The trig kicks in when the angles aren't 90 or 45 and somebody hands you a drawing that says 37 degrees and wants it by Friday.

On the prep question, I'd do a little now rather than waiting. Don't grind through months of videos, just spend a couple weeks on right triangle basics before classes start. Any free video series that sticks to finding sides and angles on a right triangle will do. Skip anything about graphing or proofs, you will never use it. If it clicks in a week, great, and if it doesn't, the instructor will go over it anyway since apparently there's a whole module for it.

One tip for when you do start: write the formulas on a piece of scrap and tape it inside your toolbox lid. Every fab shop I've been in has one guy who does that, and nobody laughs at him because he's the one who gets the layout jobs right.

Hobbyist here with a small garage setup, and what helped me more than anything was forcing myself to sketch the triangle on paper before touching the calculator. Half my early mistakes were from labeling the sides wrong, not from the actual math, which is embarrassing but apparently common. Also worth checking that whatever calculator you own actually has sin and cos buttons, because the basic one I bought for shopping lists obviously didn't, and figuring that out mid project was annoying. I'd lean toward doing a couple weeks of prep before class like the fabricator said, since rusty math relearning in a lecture hall sounds worse than relearning it on my own schedule.

Gotta push back on the 'couple weeks before class is plenty' take. I came back to school in my thirties after a decade out of any classroom, and the trig itself was fine. What ate up my time was basic stuff I'd let rot, like messing with fractions and decimals on a calculator without fat-fingering somethig. If the OP has been away from math for fifteen years, I'd spend that prep time on arithmetic and a tape measure first, then look at triangles. The sine stuff comes back fast once you're warmed up, but rusty everyday math makes every single lesson slower.