Q: switching PCs and re-installing the game

[MOZZYSTAR]

Hello,
Really couldn't figure out where I should post this topic so I apologise ahead of time if this is the wrong forum for this question.

My laptop is dying and I plan to replace it soon and I plan on taking FFXIV with me (of course!). However, will I need to re-buy FFXIV in order to re-install it? I've already bought it twice. The first time was when it initially came out (I bought a hard copy) but I ended up uninstalling it. A few years later - still having the original copy I initially purchased and its code - I tried to re-install but to no avail. I couldn't because I had already used its key(?) code (or some sort of code). So I bought FFXIV again - this time a digital copy.

Will I be able to re-install the digital copy on my new PC? Or will I have to buy it a third time?

Thank you ahead of time.