CE here with only FE (only 25) I taught myself programming in my free time as I work for a state DOT with a decent amount of free time. One of the cool things about CS (specifically data engineering/science) is it sort of is / will be permeating every technical field so you can sort of combine the two.

If your asking about the order I learned things I got pretty good with python for 2 years, tinkered with web stuff intermittently, then started programming in go and that is easily my favorite. I always always focused on geospatial programming which is at least tangentially related to CE.

The cool thing is you can start to see problems and build stuff to fix it in your free time, for example, this is something I built that gives mile points out in the field locally (no service needed), when normally a $800+ DMI is used to the same thing at a much hackier level.

TL:DR; Depending on what your wanting, I don't think you need to go to school to get competent at CS (although I'm sure I lack some fundamentals), just sort of hack on problems that interest you. Also I have had job offers for software / data engineering positions so I am employable in the field as well I guess.