Those types of connections are CRITICAL in the age of scorched-earth AI centric hiring. I spent 9 months recently jobless after getting laid off, and its damned near impossible to get a job through the usual resume farm (LinkedIn job board and the like).
Also, look for jobs local to wherever you are that don't look all that glamorous. RTO is a big thing now, and smaller organizations struggle to hire locally without the brand recognition of the big guys. That might be your in for your first job.
And the biggest thing, keep your head up. Keep pushing. You just got a degree from an extremely difficult program, and you can hang your hat on that. The factors affecting the job market are not within your control, and your skills will outlast them.