Please help! I think this is dying.

[elephanthawk]

It's some sort of cacti I got gifted a couple of years ago I have no idea what type.
It was barely 4 inches tall when I got it and just kind of sat on/in the pot.

It's really shot up recently and fell to one side like it can't hold its weight up. I repotted it and put a little bamboo stick in the pot and tied it to the plant to keep it upright.
Then the bottom leaves started drying up falling off as you can see on pictures there's no leaves left at the bottom and it was full.

Stick has struggled and it's grown even more but I'm worried about the falling leaves.

Have I killed it? Does it need a bigger pot? Is the bamboo stick the correct way to keep it upright?
How do I look after it?
I'm terrible at this

No, it isn't dying, but is desperately stretching for more light - called etiolating.
I'm guessing that it's an Echeveria - possibly E. 'Perle von Nurnberg' which is a lavender colour (might also be Purple Pearl).
The remedy is to cut the top off about an inch below the top leaves, root it, pot it up, and grow in a very sunny position - your sunniest windowsill.
To root it, allow the cut stem to callus for about a week, somewhere in the shade, place it in a very gritty potting mix, and water sparingly. In fact, the top cut may even send out roots on its own , they root very easily at this time of year.
As a succulent, it requires very good light to do well, and not to be overwatered, which can rot the plant.
I've attached a pic of my plant of this variety (grown in a greenhouse) to show how it should look when grown well.

And to add - you can also root detached leaves, which will grow a little plant of its own, but much more slowly.

Mine is doing this, but it’s been on a sunny window sill for months and started doing it when I moved it. I dislike cacti 🌵.

Here's what it looks like at the top.
It never looked like yours @NanTheWiser the leaves were always more sparse but I'm not sure where it was bought.

So are you advising me to cut the top off and try and root that on its own in another pot and keep the bottom for it to keep going in the current pot too?
It's in a sunny spot and was full of leaves before I repotted it I don't know if maybe it doesn't like the soil...
Is it supposed to grow this tall?

Seeing the top view, I don’t think it’s the variety I mentioned, but it is a closely related plant, and my advice would still be the same.

So, yes, cut the top rosette off, allow it to callus (letting the cut stem dry and heal) for about a week in a shady place, then place it in a pot of gritty potting mix (for good drainage, you can add grit to your usual compost, about 50/50) and start watering, but don’t drown it. It should recover and grow nicely. The stem That’s left might also produce baby plantlets along the stem. These can be removed and rooted like the top cut too.

Thank you @NanTheWiser I'll try that. Can I ask what should I be expecting going forward if all goes ok?
Will it be growing up like it has up to now? And how do I proceed if it gets too tall again?

Unless it gets full sun, it will slowly elongate again, I think. In which case, you could chop it again.
It’s always a bit of a problem growing succulents in the house, as light levels are much lower than in a greenhouse, even on the sunniest windowsill, but you can only give it the sunniest position you’ve got.

I put my succulents outside over the summer and they perk up a lot. I also do cut off the tops as nan says and re root them when they stretch over the winter- they root incredibly readily.

And, just to add a note of pedantry, it's not a cactus. It's one of the "other succulents" in books with titles like "Cacti and other succulents".

I agree with advice above. It needs more light. I have my succulents and cacti in front of my South facing window.