The new Legendary mods don’t start dropping until around level 62, so before that, you’ll only get the old drops (Bunny, WTF, Cracked Sash or special skin). After that, it does seem like I get a Legendary mod the vast majority of the time, but I do get one of the other drops occasionally.
As for the pearls, I have very little data to back this up (so far), but I think the drop rate may increase dramatically at OP8. I got an OP1 Wanderlust from a tubby at one point. After that, I farmed tubbies at various times, with various characters, and killed many, many of them. I only have one OP8 character. The others are all 72 or below. So probably pretty much all of that tubby farming would have been at level 72 or below. It was around 14 months before I got another pearl from a tubby (a Butcher).
But then some people in the old forums were saying that they got pearls from them pretty regularly, and they were playing at OP8, so I tried a bit of OP8 farming. It took about 10 tubbies to get a Bekah, and then I got an Unforgiven 2 tubbies later. That’s either a huge coincidence, or the drop rate is much higher at OP8.
FWIW, after that, I tried a bit of farming at OP1 and OP4, just to see if there was an increase in the drop rates when you got into the OP levels, in general, and I didn’t get any pearls, but I didn’t do that much farming. I’m just looking for random tubby spawns, so it tends to be a slow process.