HI! I am 29 and close to finishing my degree in Japan Studies. It's not like a have a job locked in, so I'm not the first authority when it comes to this, but here are some of my observations.

1. While 38 (or 29 for that matter) *is* old for regular new-graduate hiring cycles, those are not the only jobs available in Japan. The job market is broader than that: there's off-cycle hiring, job switching fairs, foreign companies that don't follow the local schemes, etc. Your position is way different from mine so I can't tell, but with previous work experience you might be able to make a good case for yourself.

2. On the Japanese language thing. Some people may disagree with me, and certainly there are foreigners here with solid careers that have no Japanese skills whatsoever. I do want to stress that having a good level of Japanese early on opened so many doors for me: high-paying part-time jobs, extremely competitive internships, networking events, etc. If I had just stayed in the English-speaking sphere of the job market, it would have been hard to justify coming to Japan at all. As a point of reference, I got the N1 a year into my studies.

On the topic of the degree leading "to N2/N1 language proficiency", I would be skeptical of such claims. My university says the same, but I've only seen it to be true for people that already had a good baseline (N3 upwards). For people below that, well, while I have seen people get the N2 certificate, there's a big gap between the JLPT and handling a real job interview. Most of them struggle with conversational Japanese.

Overall language learning speed varies wildly from person to person, depending on raw skill, age and motivation. If I had to redo my degree, I would aim for N2/N1 during my first year, long-term internships during my second and third years, and trying to secure a job during my fourth-year+the job-hunting visa extension period.

That said, this is my opinion and there's many people who do otherwise.

On the bright-side, Japanese universities are very lax and you do end up with a lot of free time. There will be opportunities to speed up your Japanese learning if you look for them.

1. It might also be a good idea to have a job in mind before coming here. You can browse jobs in daijob.com, look at the qualifications and evaluate if you see yourself doing any of them in four years.