I know it's been about 4 weeks since I switch lights but some people say don't start counting weeks until you see bud formation
Well that depends on what you want to scale, or say.
For just telling somebody at where you are, it is enough to say when you switched the lights.
Depending on the quality of light, the introduction of the flowering can take longer or be shorter.
Thats why usually to determine the point at where you are for feeding etc... the actual state of the actual flowering matters, not when you switched the lights.
you count from the first signs of flowering to find out the actual state.
I think thats not bud-formation but the first calyxes with stigmas showing up on the internodes.
Sometimes these show on old plans in veg already and so they are instantly into flowering with switching the lights.
Usually i see them first about 1 week after switching the light from cuttings having 3-4 weeks from the point of cutting... and then I start counting the weeks that the breeders say. And that is always ON POINT with any strain.
Thatway you take out the "flowering introduction" time.... that is important to determine how far you really are, to take the right decision at the right time, not to late or to early.
The breeders always count from the first signs of flowers for the given duration of flowering.
PS: For example with NIR from the first day of switching the lights to 12h..... introduces the flowering significantly faster than without NIR. That saves you time, of the actual total flowering time, when the first signs start earlier say 2 or 3days.