Just start somewhere. These guys are making changes, actual functional changes and bug fixes in that environment meaning they already have all the problems you imagine are going to get in the way of fixing this mess. So stop fretting and just start small with one tiny thing. It doesn't really matter with what. You don't even need automated tests necessarily. It's a small simple flow that needs 10 minutes to run the same test steps manually for? Write them down and do it manually, I don't care. Just Do it.
Been there, done that. Slightly differently where they had a test server and prod server. So already better except one day I made a change and copied to prod. Yes it was manual. Just scp the files over to prod. And stuff broke. Turned out someone had fixed a bug directly in prod but never made the change on the test server.
First thing I did was to introduce version control and create a script to do make deployment automatic meaning it was just a version control update on Prod (also scripting languages here). Magically we never had an issue with bugs reappearing after that.
Pretty simple change and you can go from there.
The above code base was over 20 years old and made use of various different scripting languages and technologies including some of the business logic being in stored procedures. Zero test coverage anywhere. You just 'hide' small incremental changes to make things better in everything you do. Gotta touch this part because they want a change? Well it could break anyhow so make it better and if it breaks, it breaks and you fix it. It needs judgment though. Don't rewrite an entire module when the ask was adding a field somewhere. Make it proportional to the change you need to make and sometimes it's not going to be worth it to make something better. Just leave it.