Official openconnect client source is on gitlab btw:
https://gitlab.com/openconnect/openconnectTo avoid this problem, once I know the name of the project, I research it to find the official site / project page and then follow their links to source.
To answer your original question, security is very complex and it's not hard to hide backdoors or malicious functionality from the uninitiated. If you're not an appsec person by trade, it's probably safer to pay to have it professionally audited.
That's usually cost prohibitive. You can try free SAST and DAST scanners for code (run in a VM or on a VPS for DAST scanning - VPS has the added benefit that if it's serious malware that includes VM escape, your system is still safe) as well as multiscanners like virustotal for compiled binaries, but do not assume that a lack of findings in those means a tool, project, or binary is safe.