I agree the job market is not flourishing as much as it did 2 years back. But things have been improving for the last couple of months.
I am completing courses, revisiting notes, sending out connection requests to product folks at different companies, practising interview questions and reading PM case studies.
After applying for so many companies without getting a revert, I believe it's wise to narrow down the approach.
I will start talking to PMs on LinkedIn and will try to apply through referrals. On job boards like LinkedIn there are a couple of thousands of applicants for every single opening. And I have heard more than 60% of jobs are closed through referrals and remaining through job postings.
Good luck!