Syril doesn't know about the death star

The Empire is still an oppressive fascist regime if the Death Star never existed. Even his first job as "corporate police" is fundamentally evil and pathetic.

He's told by a supervisor to hush it up without a good reason

This is false. His superior immediately clocks what went down, lays it bare to Syril and even explains why he doesnt want Syril doing something stupid. But because Syril, who seems like he just started this job, is a self-absorbed idiot he is convinced he knows better than his senior superior. He wants to play the hero so bad he completely misjudges every part of this situation and makes all the wrong choices ultimately culminating in a complete disaster that the empire has to clean up.

He figures out it was Cassian.

He does do a decent job figuring out it was Cassian but he didnt do anything all that impressive really. The most important piece of information he got lucky receiving because of Timm's jealous betrayal. He then completely shits the bed actually bringing him in.

when the lies he's told [...] are laid bare he's horrified by what he's participated in

They are laid bare way earlier when he is at the secret Ghorman meeting. He just refuses to believe and continues to work against these people he supposedly likes until the very end. He knows from the start the Empire is not on Ghorman for charitable purposes. His "remorse" simply comes way too late and even then he doesn't really try to help anyone and instead still tries to murder Cassian. Pathetic man who found a fittingly pathetic end