The UI Audio pack has a lot of "clinky" sounds that could work for pieces being moved. kenney.nl/assets/ui-audio
The Casino Audio pack doesn't have many particularly useful ones as it is filled with ruffling through cards, though the dice throws could be used for moving pieces and maybe some chip throws could be used for capturing. kenney.nl/assets/casino-audio
The Digital Audio pack has some that could make for a cool space-themed audio selection. I imagine the files labeled laser.ogg could be used for check while pep and jump could be pieces moving. Powerup.ogg or SpaceTrash.ogg could be used for clock warnings (If that audio is replaced) kenney.nl/assets/digital-audio
I just downloaded the folder and opened all related audio in a VLC playlist and listened to all sounds within 5 minutes. I suggest looking further into using sounds from the Digital pack. I'm happy to assist anyway needed.
Either identify/acquire a FOSS license for the standard sound set, or replace it.
A recent BLM bundle on itch.io (now ended) included https://kenney.itch.io/kenney-game-assets-1 ; https://lichess.org/@/ChesswurmOTB says about it:
https://lichess.org/forum/lichess-feedback/what-are-the-rights-for-the-standard-lichess-sound-effect-2#7