I'm a mechanical engineer and I believe I can answer your first question. My take is that many engineering employers value the ability of entry-level employees to learn new things rather than what they know (their expertise). They want blank slates many times, to be honest, to be molded into the kind of employee that they need at the moment. As long as you have the most basic relevant engineering knowledge and a degree you are good enough. For example, my first engineering job was actually in chemical engineering largely (chemical kinetics), and I got it despite knowing very little about chemical engineering.
This is both good and bad for the employees in my view. It is good in the sense that you could (potentially) change subject matter easily, but it is bad in the sense that you are very much replaceable. That said, many employers do want and need specialized knowledge and experience even for entry-level engineering positions (not just for experienced positions), and any entry-level candidates with that specialized knowledge and experience will do better in the hiring process (as far as I know!).
That said, my recent experience in the job market actually matches bserge's experience. There are far too few open positions in my observations, and I too had to apply to way too many jobs, and it took far too long to hear back [1]. That is of course just another anecdote but it has been my experience as an engineer. I'm gonna be fine and will start a new position soon, but I think the narrative that there is an employee shortage only applies to low wage and unskilled workers and not to engineering professionals.
[1] I recently started collecting data on this from my own job applications. For example, the median number of days to a final decision for me was 55 days. The mean was 112 days. This appears to follow an exponential distribution. I only started looking into this data recently when I questioned why it took 4 months for an employer to request an interview with me.