Lucky I only race CX / XC and my cross bike does actually have the sticker anyway!
Luckily if I ever want to give a road race a go my Tarmac will do the job, sounds like CX is more chill. Until you get to high level.
having said that I was just re-watching the 2022 CX worlds and they were only checking for 33mm tyres
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That 33mm tyre rule is a pain. It’s probably better with tubulars, but you can’t even just rely on the stated tyre widths for tubeless. Challenge Grifo & Limus 33 both come up a couple of mm wider on my Hope 20Fives 
I’m on spesh terra pro, which weirdly come up as exactly 33mm for me on those Hope wheels, but I know someone much faster, who says they are too wide on the same wheels. Luckily I’m unlikely to get checked in most of my races.
Tyre width checks are standard at all races directly under UCI rules. Other checks are more rare.
If you watch the junior men’s world champs, you’ll hear about British lad Nathan Smith, whose bikes (Ribble CX) weren’t UCI approved, so he couldn’t use them. Luckily he got lent two Trek bikes, so could race. He’s raced on the Ribble bikes all season, national champs and even a world cup, and never got asked about it before.