It’s basically stuck at
[FNILJ] INFO: Relay listener (dynamic+https://relays.syncthing.net/endpoint) starting
[FNILJ] INFO: Relay listener (dynamic+https://relays.syncthing.net/endpoint) shutting down
[FNILJ] INFO: listenerSupervisor@dynamic+https://relays.syncthing.net/endpoint: service dynamic+https://relays.syncthing.net/endpoint failed: Get "https://relays.syncthing.net/endpoint": tls: failed to verify certificate: x509: certificate signed by unknown authority
in a loop.
Which Android version are you running? Is this the stock ROM? If yes, then it’s likely very outdated, so I think that you may need to do https://forum.syncthing.net/t/x509-certificate-has-expired-or-is-not-yet-valid/17617/7 (which requires root access though).
Otherwise, you need to run an up-do-date Android version, which means basically installing a custom ROM. For example, DivestOS (https://divestos.org) supports Nexus 7 (2013).