There's really two parts to worry about: getting an interview, and then passing the interview.
The getting the interview part is difficult: some places will more liberally interview candidates, and others more heavily screen them. The three things that you can change to improve your odds here are tailoring your resume to use more words and phrases from the job description (trying to game any AI or human resume screener), networking to try to bypass the screening stage altogether, and casting as wide of a net as possible. Networking can be anything from having a social media presence, going to various forms of dev events, talking to friends about open roles they've heard about, or even cold emailing people you're interested in (although, if you do this, you'll probably have more luck asking to zoom/coffee for career advice than asking if they have a job available for you). And then, regarding the role you're targeting, I moved into increasingly technical roles starting as a data analyst-- I know not everyone would agree with this approach, but it worked well for me. I was a really technical analyst, who became a data scientist, who worked up the ranks, and then started moving between DE/MLE/DS roles. But this was also back in the days when "data scientist" was a new term, and before it got so watered down-- so maybe with title inflation, my original "data analyst" jobs might be "data scientist" jobs today? Anyway, my point is that I think it's easier to slowly slide in to your ideal role than it is to try to hop directly into it.
The passing the interview part ends up being so much about how you communicate and frame work that you've done. It sucks because this ends up inadvertently screening out really smart/good people that struggle with this kind of thinking (and screening in people who are good at talking but suck at doing e.g., many MBAs). But once you're talking to a live person, I think emphasizing how your degrees (both grad and ugrad) have really prepared you for exactly the role in front of you. You can also often take non-technical experience as evidence of certain components of the technical job requirements. Like, I worked in a restaurant when I was a teenager, and you better believe that prepared me to deal with many concurrent demands from many different sources, and required me to think on my feet about the priority/order of operations. So, when I was earlier in my career, I got really good at answering questions along the lines of "you know, I haven't done this work in a single role, but I have experience doing everything you're asking for over multiple roles..."
But it sounds like a lot of the issue you're running into is just getting in the door to begin with? Unfortunately, I think so much of it comes down to luck-- just keep applying to as large of a variety of jobs as possible, and network as much as you can.