That’s the point though.
There aren’t any half elf mechanics.
Nothing a half elf gets in any way indicates a half elf. Dragonborn get a breath weapon. Tieflings hell ish rebuke. Even halflings are lucky.
A half elf gets the same thing you get with every single background. Two skills. Because nothing says I’m a half elf like proficiency in athletics.
Yes there are. Those half-elf mechanics are a bit of human mechanics and a bit of elf mechanics.
The above do indicate half-elf and also half-human.
And no, there are no backgrounds that will allow you 4 background skills. The two half-elves get are for race, and they ALSO get the background. So it looks like this.
Dragonborn cleric with folk hero background:
2 skills from history, insight, medicine, persuasion, and religion.
2 skills that are animal handling and survival.
4 skills total.
Half-elf cleric with folk hero background:
2 skills of choice from race.
2 skills from history, insight, medicine, persuasion, and religion.
2 skills that are animal handling and survival.
6 skills total.
There no background that can allow the 2 bonus half-elf skills, because the half-elf also gets a background.