Laravel + Vue, Filter with Vue Only or Filter with Api Calls?

Hi,

I'm learning Laravel API + Vue right now, and I have a list of products and categories. Now I wan't to create a filter with Categories, but I'm running into a dilemma. Should I filter with Vue Only or Filter with Api Calls?

Filter with Vue:

Get all products with API then filter them through vue. It works, but if I have many products then the API call will take too long and I guess high memory usage as well. I could paginate the API, but then the filter would work on the paginated products only, not all products in DB.

Filter with API:

I found this tutorial: https://www.youtube.com/watch?v=ZZkROqT83t8&t=338s

Firstly, I'm finding it a bit difficult to understand how or why it's working. Second, I cloned the repo to test it out, and if I keep using the filter frequently, it runs into 429 Too Many Requests error, so I don't know if this is the proper way. Here: https://youtu.be/_6j7Lgd1ZyM

So, which option would be better, and is there a more in-depth tutorial on this topic?