I am in a similar position (career transition at 37yo to software development), mostly self-taught through the internet (freeCodeCamp and building my own stuff following documentation and tutorials online). I still haven't got a job, so I can't say I have a good answer for you. I am just speculating from a similar position. I don't think I would even apply to fancy, well-known companies that lots of developers coming…
I worked at a web agency before so I know how that is. If software is just a means to an end, what are they exactly selling if not software? Websites as a service, perhaps, but that still doesn't support the business model that focuses on hourly billing, that puts a perverse incentive for developers to produce less satisfactory results.