I got myself a business number between my last job and my current one, because I wanted to have the option of working as a consultant to others on a gig basis until I found a new full time job. That was nearly 25 years ago. I told my employer about my side consulting business from the beginning, as I was hired on contract at the outset. I have had several occasions when a client at work asked us to do work which was outside our area of interest but related to mine from past employment. I carried out the work privately for the client with my employer's knowledge and blessing.
There is nothing wrong with doing something else for money in addition to being an employee, as long as you are not in conflict with your employer- and you're not hiding anything. My first conversation with any potential side client is, "I'm employed by X, and any work related to X's practice which is areas Y and Z, I can't do for you- it will be handled by X Inc." Of course some employment contracts attempt to restrict any secondary employment including self-employment. I am unburdened by such an agreement. Doing work in contravention of an employment contract is pretty much the definition of "conflict with your employer".
You also need to keep your need for insurance and/or voluntary liability limitation in mind. If you're paranoid about liability, you need to set up protections against that which will mean you will need to really do quite a bit of work just to cover the fixed costs of your side "business". Most full-time employees find that to be a deal-killer right there.
There were times when I did no outside work, because the main job and the rest of my life left me no time. Once the kids got older, it was possible to pick up little bits of work on the basis of relationships and interest. That will continue for me into retirement.