Star Wars Jedi: Survivor players are able to customize Cal's lightsaber, even being given the option to change the color of the blade. What you can't currently do is turn Cal's lightsaber into a darksaber, although one player has encountered a glitch that has done that for them.
Tontongas took to the Fallen Order subreddit to share a clip in which they use a white-bladed lightsaber to attack some Bedlam Raiders. However, the lightsaber is black instead with a white glow, making it look a lot like the darksaber that has been integral to the plot of The Mandalorian.
No, I don't think Cal is now the true ruler of Mandalore. I also don't think the darksaber has ever been featured in a Star Wars game before even though its existence in the franchise's lore pre-exists the Pedro Pascal-led Disney Plus series. I do need to check if it has been added to The Skywalker Saga, though. So much stuff has been thrown into the Lego game post-launch that it may have snuck in there.
Some of you aren't convinced this isn't its secret debut in a video game though, accusing the glitch of being a mod. The OP has astutely questioned why they would claim a mod they put a lot of work into is actually a glitch while others have confirmed there are currently no mods that change the color of Cal's lightsaber in Jedi: Survivor. Tontongas has also shared more screenshots in the replies demonstrating other white lights affected by the bug. Cal can be seen standing in front of an essence in one image, the white light it emits smattered with black patches.
This may well be the first example of a glitch Survivor players actually want. Most of the problems suffered by the Fallen Order sequel since launch have been undesirable as Respawn has scrambled to fix as many of them as possible. EA revealed there were weeks of patches planned before Survivor even launched, and while the issues have been more extensive than expected for some, players knew the game wasn't going to be perfect out the gate.
You would think just a month after launch, most people would still be working their way through Jedi: Survivor, especially with Tears of the Kingdom's arrival coming since. Just a little game to distract you from your Star Wars journey, right? However, one player is so adept with a lightsaber in their hand, they've already managed to beat the game on Grandmaster without taking any damage. Others who have finished the game are already discussing what the next game should be called.