What tools would you recommend for managing Vulnerabilities and Exposures in an environment utilizing CrowdStrike and M356 Defender? We are also looking for tools that would work with a SOAR and possibly a ticketing system.

Seemplicity is a good choice in this space for many orgs  https://seemplicity.io/

We use Rapid7's IDR (detection & response) & IVM (vulnerability management) in conjunction with Crowdstrike for endpoint protection (we do not run M365 Defender as well). We also use Rapid7 for orchestration (SOAR) to automatically deal with a range of security event types. Been very happy with the outcome, which we utilise through a partnership with a local SOC. We also recently transitioned to M365 E5, so are currently assessing how Microsoft's security features may add to our overall posture, but I don't see this replacing what we have. Also a big fan of Wiz, which provides similar vulnerability management capabilities for our cloud assets. Hope this helps

Using 2 XDR vendors in the same environment?
Sounds like a common use case for SGNL but can't be certain.