One of the things races really need to be more significant is more proficiencies, or rather for them to not exist in the same space as class/background bonuses, you have proficiency in acrobatics from both race and class? Congratulations you now have expertise, already have expertise? Triple proficiency? Natural advantage maybe? I dunno but something so that the bonuses are additive rather than mutually exclusive.
Picked a dwarf with a class that already gets med/heavy armour? Then get a flat +2 in addition to the regular AC score it provides, same thing with racial weapons but with To-Hit
Got Elven longbow training but your DEX score was (somehow) your dump stat? For the purpose of using longbows your DEX mod is considered to be 1/2 proficiency bonus!
I do think some scaling would be good too, the dragonborn’s breath weapon increases in damage, halflings start with only on use of lucky per day but gain more at higher levels, resistance becomes immunity (becomes absorption?)
And finally, spread their traits across multiple areas, PHB dragonborn was cool but with only a breath weapon and resistance (yes im aware it got buffed later i think but my point still stands) the fact you were DB didn’t actually come into play all that often mechanically so it was even easier to forget that you were actually a DB.