I think as a mechanical engineer, your prospects are good. Many places will look at any kind of engineering background as "good enough" and then want to start talking about code or process or whatever their interview is all about.

In my opinion as a 20 year software veteran, the skillset many software engineers lack is having a bigger world-view of company operations and why they are doing what they are doing. Some of that is obviously on the company structures they've been exposed to, but decent engineers with really good business sense go far, fast.

As johnwheeler said in this comment section, just start building something. I bet it comes to you pretty fast, and if you have an engineering brain, you'll start seeing the pieces move in your head just like any other system. I really don't think you need "retraining" per se, just start applying your business sense and engineering skillset to software. Consider even looking for companies where both are required, like places that build mechanical things controlled by software, and look for roles that offer the potential for some cross training.