I think in the case of classes it is who you do not get as a companion or do not use as a companion. As for races, half-elves and humans were always the most popular (in that order, I'd say) and all "shorties" were always in a minority.
Have to admit, Dragonborn ahead of tieflings did surprise me here.
Humans have always been pretty popular. However, Half-Elves were not always popular; they were only popular when they didn't suck. At least that's my recollection. Elves have always been pretty popular but they have also never really sucked.
The reason I think Half-Elves are pretty popular right now is probably because of Shield Proficiency. (Humans get that, too.) The 2nd, 3rd, and 4th most popular class choices all benefit from a Shield Proficiency more than just about anything else. Humans don't make good Paladins, but Human Paladin has been a thing since the early days when only Humans could be Paladins. Wood Elves are good at just about anything because they are fast in addition to getting their other racial bennies. I'd like to see the cross-tabs on it, but from my subjective view, a Wood Elf Paladin is a synergistic combo due to speed and a Human or Half-Elf is a synergistic combo with Sorcerer, Warlock, and Rogue (for the stupidest of reasons: Shield Proficiency). I think that is a pretty good partial explanation for why the top 3 races and top 4 classes are where they are.
The mid-tier races (Dragonborn, Tiefling, and Drow) are all "cool" choices that don't have a significant downside (like reduced speed) and don't have poor synergy with many classes. Most of the classes fall in a middle range of popularity (with the Paladin, Sorcerer, and to a lesser extent Warlock standing out above all others) with only the Cleric being unpopular.
The shorties are all slow, which is a pretty big ding. I think you could fix the problem with shorties by making them better. If Halfings got a free proficiency in Stealth, that would help. All Dwarves should get a Militia-like Trait for Light Armor and Shields (which only makes sense if Humans and Half-Elves have it) and, for Shield Dwarves only, an Armor Proficiency after class has been chosen, to bump Light Armor to Medium Armor, Medium Armor to Heavy Armor, and Heavy Armor to Heavy Armor Master. Gnomes should each get Expertise, like Rock Gnomes get Expertise in History and Sleight of Hand (they lost the 5e Tinker ability, after all), Forest Gnomes get Expertise in Animal Handling, and Deep Gnomes get Expertise in Stealth.
Githyanki in 5e have Resistance to Psionic Damage; bring that back. Currently they are about the least synergistic race for Fighter, which is ironically what Lae'zel is. At least give them something.
Clerics are boring, but they aren't weak. I think making them stronger would be a mistake that has been made before, resulting in CoDzilla. What you could do is give them a couple of unique Cantrips. Like a Cantrip that allows you to help a downed ally at a distance (like Spare the Dying but at a distance or maybe at Touch range but as a Bonus Action because everybody in BG3 can take an action that is equivalent to the Spare the Dying Cantrip) or an offensive cantrip as an alternative to Sacred Flame (like Word of Radiance).
