Aikido is actually quite limited in its scope. There aren't many kinds of strikes, take-downs, and throws.
Hapkido has a lot more striking than Aikido does, and a lot more types of throws. But it, too, is limited.
When someone says there are thousands of techniques, what they're referring to are variations and combinations. But to get to that high count, you start with a small collection of basic techniques, and then you change the way they're done using one or more different concepts or principles.
In Taekwondo, for example, you have an inside-to-outside crescent kick. If you spin around and then do that kick, it's called a spinning, inside-to-outside crescent kick. If you hop forward while doing it, it's called a hopping, spinning, inside-to-outside crescent kick. If you jump while doing that, it's called a flying, spinning, inside-to-outside crescent kick.
You could take any kick and do the same thing. The kick is the basic technique, while the spinning, hopping, and jumping are concepts that change the way that kick is used or expressed.
In my answer at the following link, I calculated 1344 different kick variations in Taekwondo for just 8 basic kicks:
How does one train for a spinning reverse kick?
Similarly, in Aikido or Hapkido, there are plenty of variations for each technique. Are you standing or sitting? Are you sinking down to rising up, internally? Will your opponent grab the arm on his same side or across to the other side? Is your opponent in front of you or behind you? Do you have one opponent or more? Do you atemi (strike) first? Can you turn this hand technique into a knife, jo staff, or sword technique? Do you send your opponent down to the ground face first or back first, to the left or to the right? Do you change levels (sit down) while performing the throw, or do you stay at the same height?
You get the idea. Every basic technique can have many variations. In the end, there might be thousands of unique techniques.
What matters is that you understand the finite and small number of basic techniques, plus the small number of concepts or principles that can be applied to change the way those basic techniques are expressed. That makes it easy to learn. You don't have to be shown each one of those thousands of techniques in order to know them all.
With Taekwondo kicks, there are only 8 basic kicks and maybe 6 different concepts that you can use to apply to each. The combination gives you 1344 unique kicks. Learning those 8 kicks is easy. Learning each of the 6 concepts is easy. And once you've done that, you can fairly easily come up with each and every one of those 1344 kicks on your own, even if you weren't taught most of them.
And we haven't even gotten into combinations.
It's the same way with any martial art.
Hope that helps.