The previous career experience is definitely useful and you'll want to draw out the interactions you've had with commercial supply chain partners and ESG/other regulatory requirements in your previous role. Make sure this comes across strongly on any applications you make.
You shouldn't get too focused or targeted on specific areas of law like shipping etc... because law firms don't recruit to that level of specialism at TC level. Based on the areas you've mentioned you need to look at the general world of commercial law firms and get applying.
Unless you want to do a LLM purely for personal or academic interest I wouldn't recommend doing an ESG LLM - It is very unlikely to make any difference to your career prospects in law, or ability to gain a TC. You'd be far better served working in a legal role (even a very basic one) to gain practical experience - this also has the advantage of earning, rather than costing money!.
On ESG more widely - Whilst it's obviously your background and an important issue facing many corporates, it's not really it's own area of law, more of a theme that touches on parts of lots of different areas of law. What I mean is that on a training contract you will not do an ESG Seat, nor will much, or even any of your work have any ESG relevance. Typically in a law firm anyone marketed as an ESG lawyer will be a lawyer with a core specialism such as corporate, property, or projects etc.. who also covers some ESG tangents as a *small* part of their role. Environmental law is its own separate area in turn but it also quite niche (with very limited seats available on a TC, if any, and teams will focus on land/chemical contamination, planning, pollution & disposal permits etc... rather than wider ESG advice.
Being a lawyer working in commercial practice is not being an ESG professional, and those lawyers who do work on aspects of ESG matters in law firms will almost always have worked for many years in their core specialism before taking on an additional ESG mandate.