How do you best approach internship search mentally?

I'm doing Masters in Machine Learning after getting a BA in Mathematics, and I've been looking for an internship. I have a year of job experience in IT, and I've been shortlisted several times for a job, but never actually got an offer. It's clear to me that this offer will come eventually, as I gain competence and experience in my chosen field, getting a few (more) minor projects under my belt.

But it's nonetheless been stressful, and I wonder if anyone more experienced than me has some tales to share about their time in the trenches. I'd especially love to hear about people who made a job switch in their mid to late 20s, which is the situation I'm in, and did it fairly recently -- I know the times were different in the mid-2010s, and many ideas that were great back then aren't so now.

I guess the key skill to learn at this stage of my career, which is not at all only specific to job search but a very powerful asset to have in general, is being okay with anything. I've been fascinated for a while with the idea that you might pursue something relentlessly while at the same time being unworried about the outcome. Has any of you emerged from your early-stage career with that kind of mindset?