Open embedding in new tab link is broken

Problem

It adds a button to open a video in a new tab (if there's a block like "log in to confirm you're not a bot") – it's great, that what I downloaded this script for! But the link is broken. It just copies the link in the embedding that not always can be played in other tab.

Example

Embeddings in https://mewgenics.wiki.gg/wiki/Eatin%27_Rats has buttons with links like https://www.youtube-nocookie.com/watch?v=id&autoplay=1 that are not correct.

The solution

replace

fyte.srcWatchFixed =
  fyte.srcEmbedFixed.replace('/embed/', '/watch?v=').replace(/(\?.*?)\?/, '$1&');

with

fyte.srcWatchFixed = 'https://www.youtube.com/watch?v=' + id;

  // If original parametrs has parametrs like start/t= (time), add them
  const timeMatch = srcFixed.match(/[?&](?:start|t)=(\d+)/);
  if (timeMatch) {
    fyte.srcWatchFixed += '&t=' + timeMatch[1] + 's';
  }

I don't understand, because the script doesn't add any buttons by design and anyway the current code doesn't remove the existing parameters from the URL.

Without this script:

With this script:

Link in this clickable text is broken by default

the current code doesn't remove the existing parameters from the URL.

Exactly, that make it broken, becouse some of parametrs are not meant to be opened out of embedding

I understand which link is the problem, but I'm not sure the proposed solution is correct, because it looks like simply dropping -nocookie from the domain name is a better fix. Could you try it?

My solution is to just replace link with standard one, removing any junk that may break the link (except time params, afaik it's the only params that can be used in new link)

I understand which link is the problem, but I'm not sure the proposed solution is correct, because it looks like simply dropping -nocookie from the domain name is a better fix. Could you try it?

For this link – maybe, but why even preserve original link? What if other embedding would have some other link-breaking things?

Thing is I don't know which parameters may be used, which is why I don't assume that the only meaningful one is start|t.