With all the info about what's been made worse compared to the original, it might be appropriate to also mention the trailer… as in, what the heck is that music?

One of my favourite and most memorable things about the original XIII was its jazz-funky spy thriller soundtrack. I mean, they have this to start from:
https://www.youtube.com/watch?v=glftUqxT8k0
and for their Attract Mode they're going with Johnny McGeneric Pop Ditty?

(With the ever-reliable hallmark of quality songwriting by a truly talented lyricist; I quote: "woooah-ooh ooh-woooah ooh-woooah")

You can just buy the original game here for a considerably low price.

I was kinda looking forward to this as I love the original XIII game. Seeing this remake on the GOG storefront when it was available for pre-order motivated me to buy the original game on GOG. It holds up really well!

This remake, from what I've seen in video reviews and reading what other people have already written about it, sounds really messy, with quite a steep price tag for what it is. It sounds like multiplayer content has been reduced and the art style/cinematics are nowhere near as distinctive. So many glitches and problems with the sound mixing too from what I've seen in gameplay videos.

I hope a patch could salvage this game because it'd be nice to see a XIII do well with a wider audience (the way that Oddworld did so well with New N Tasty that it's now rebooted the franchise, a new game coming soon) and for us to someday get a XIII sequel, but right now I won't buy this version of the game. It just looks like it needs a lot of work done to it. I'm sure the devs worked really hard too, and I feel so sorry.

You have more chance of a patch solving world debt than you do fixing this game. It's fundamentally broken.

https://www.thesixthaxis.com/2022/06/30/xiii-remake

"XIII remake is being remade again

Following the disastrous launch of 2020’s XIII remake, publisher Microids has announced a major upgrade coming later this year. This is effectively another pass at modernising the 2003 comic-inspired shooter

Originally developed by PlayMagic, the project has now been passed to French studio, Tower Five, which has been working on the XIII update “for more than a year”. The free upgrade will be available from September 13, 2022.

When it launched on PC in November 2020, XIII was mauled by disappointed fans and reviewers, bagging a poor OpenCritic average score of 34. Dragged down by myriad technical issues and a confusing change of art direction, it was quickly labelled one of the worst remakes/remasters of all time.

Microids was quick to issue an apology, patching the game to remedy many of the bugs players had flagged. Fans won’t be quick to forget the game’s disappointing launch but at least the publisher has gone out of its way to try and rectify its mistakes.

“We are fully aware and terribly sorry that the initial launch of XIII Remake on PC did not reach players’ expected quality standards,” said Stéphane Longeard, CEO de Microids.

A bit more than a year ago we took the decision to hire the studio Tower Five to finish the development of the game. Tower Five worked with us in the past, notably on the great port of Agatha Christie: The ABC Murders on Nintendo Switch. We really wanted to take the time to fix the game and offer owners of XIII Remake a free update paying the best possible tribute to the original game we all love.“"

I would advise people to still not buy this game. Aside from the art style, nothing has really been improved, and while it's not as buggy as it used to be, it's still very bland and not as fun as the original.

Have we got the remake remake then?

If you didn't like the original, there is no way you'll like this one.
In this regard, maybe they did a proper remake after all.