My brother broke my old laptop, and I recently purchased a new one. I want to sync all of the photos that I have on my mobile app and that I can see in browser to the program installed on my computer.
I cannot copy the catalog from the old computer because he spilled water on it.
This forum (Lightroom SDK) is about writing Lightroom plugins, i.e. SDK stands for "Software Development Kit". It's not a very active forum, since there aren't a lot of us using the SDK, so you'll reach a much wider audience in the main "Lightroom" support forum, Lightroom Classic CC — The desktop-focused app .
That said, I would remove the hard drive from your old computer and try to transfer your files from it. It may be okay, even in the computer is fried. You don't mention the OS in question, but on Mac, at least, this is quite simple and can (or might) allow you to transfer all your user data. You could even take your old hard drive into a new computer, if there is an available drive bay that you won't (often) use, otherwise, e.g. an optical bay (probably easier to do on a Windows-based machine, since a new Macbook hasn't had an optical bay for a while). If you were running from an encrypted drive, it may offer some additional challenges, but I would at least see if you can restore from your old drive before assuming all data on your old notebook has been lost.
Lightroom is mostly for working on your RAW images, so syncing from your uploaded (and lower-resolution) JPEGs would probably mean you are giving something up. I've never even used the mobile app, so I won't provide any advice here. ;-)
In future, I highly recommend using a good backup program and storing copies of all your original files on an external drive.
Hope that helps and best of luck.