So of course this is only anecdotal but I've never sent more than 5 applications out at a time even back when I was a junior dev. In the last 10 years I don't even bother looking for jobs actively anymore, I just turn the switch on my LinkedIn indicating that I'm seeking employment, and let recruiters do the rest.
I'm not sure what the difference is, but I would consider myself to be an outlier as far as traditional engineers go, in that I am both exceptionally articulate and naturally extroverted. If I can get to the point where I have a face-to-face or a phone interview, I'm fairly confident that I'll be able to acquire an offer. Without specifics I can only recommend that engineers work on developing their soft skills if they don't already have them.
On the other hand I'm not particularly picky in terms of companies, and I have a wide range of senior level experience in major platforms including C# and node/typescript/JavaScript.
Just a counterpoint for all the gloom and doom but I'd say that you have nothing to worry about if you have the following:
- in demand skillset (ts/js/c#)
- people skills / charisma
- US citizenship
- 10+ years experience
- reasonable salary expectations (140-175k)