That would depend on your settings and on your OS.
Syncthing can be set up to use Trash or versioning. Did you enable that?
And, depending on OS and filesystem, there are methods (not syncthing related) to recover deleted files.
There is no real “send to trash” option, but a file versioning option which behaves like that, but puts the files inside the .stversions folder inside the shared folder.
The benefit of the current trash file versioning is that it is universal and works on systems without a system trash (e.g. mobile).
A custom file versioning which moves to the system trash could work, of course.
There needs to be a different script for each system type / trash implementation.
The problem I see in using the “real trash” is with edits (in contrast to deletes):
How does the system trash handle a restore where the original file is still there (but different)?
How does the system trash react when moving the same file (with different content) to the trash?
That, and also that we can have our own policy in terms of when to remove stuff (i.e. automatically after a week and so on). That means it can run unattended. Otherwise you’d essentially end up with a full copy of the synced folder in the trashcan after a while, if there wasn’t someone there to take out the trash now and then.
People keep trying to use Syncthing as a backup solution when it is not one. I can’t wait for everyone to have COW filesystems with easy rollbacks. It’s clear that 95% of people can’t be bothered to actually backup and filesystem snapshots would be good enough for them.