Job searching while pregnant

I work full time and have been at this job 5 years. I like the people, but I’m not motivated and am bored. I’ve been searching for new jobs - not super hard, but have set up job alerts and look here & there. I found one I’m interested in, but I’m not sure what to do for a few reasons:

- I’m due May 24. With my current job I have enough time saved to be paid the full 12 weeks (whoooo parenting in the US 🙄)

- will they hire a visibly pregnant person?

- in my current position I have good benefits (health insurance and retirement) that I would be trading for maybe not as great in the new job

Is it worth applying and trying to get an interview to learn more? Or should I stick it out at my current job, have my baby & paid leave - then really begin a job search? Any advice - thank you!