What's a good way to sync project and university files between two computers?

Cloud storage is probably the simplest change. A sync client for Dropbox, OneDrive or another provider can keep selected folders available on both computers. Google Drive can work too, though the client options depend on your operating systems. Insync is one option mentioned for Google Drive on Linux.

Give the first computer time to upload before leaving, and let the second finish downloading before editing. If both copies get changed before syncing, you may need to resolve a conflict.

You might not need to replace Syncthing. Set it up to start automatically on the computers, then they can sync when both are online. If their schedules rarely overlap, an always-on machine at one location could act as another device holding a copy, so you don't need to carry the laptop just to transfer changes.

That keeps the setup peer to peer rather than relying on cloud storage. Check that the devices have finished syncing before you shut them down.

For code, I'd separate versioned source from the other files. Push commits to a Git remote and pull them on the other computer. Use a file sync tool for notes, PDFs and art assets that aren't practical to handle that way.

Git isn't automatic folder mirroring, so you'll still need to commit and push your changes. It does make the history of code changes easier to manage.

If you're comfortable setting up a machine as a server, SSH gives you another route. You can access files remotely or use rsync to copy them between computers. Tailscale can help connect the machines without treating them as if they're on separate networks.

That approach needs the server to be online when you connect. It's more hands-on than a sync client, but useful if you'd rather pull files when needed than mirror everything automatically.

Rclone is worth a look if you want to use a cloud provider but prefer a command line tool. It can copy files to and from supported storage, and its bisync mode is intended for two-way synchronization.

It takes more setup than a typical desktop sync client. Test it on a small folder first, especially before using two-way sync on your only copies.