They exist, but they don't pay well.

The piecemeal contract work that is time-limited and doesn't require any prior relationship usually goes to the lowest bidder. It's you versus a hundred people in other countries with 1/10th the cost of living.

Moving to a higher paying job is the fastest way to bump up your income. Freelancing can augment it, but it's a bigger commitment than what you're describing. Most clients won't be interested in you doing little bits of work as you feel like it. They want things on predictable, rapid timelines.

I came to web development from graphic design via web design.

I don't really do it anymore, but even after transitioning to full time development (mostly backend) I used to pick up small design jobs (such as logos). Some of that was pro-bono work for or related to open source projects, but much of it was compensated at fairly reasonable rates.

I've found that design work usually wasn't needed on a tight schedule, which made it easier to schedule around a full-time job, and having a shared technical vocabulary with the clients (and being present in the technical communities they frequented) gave me an edge in landing the business and getting paid up-front. I haven't tested this proposition for a while, but I would be surprised if it doesn't still work.

Now, you may feel that you aren't a designer, but good design isn't any harder to achieve than good code. Great design, like great code, often requires a little extra something, but we're really talking about 'doing design' rather than 'becoming a designer' here. A little coding effort can go a long way in terms of procedurally generating variations on a grid in order to narrow down the search space to a few that 'look right' even though you aren't sure why.

The 2nd time I took a long time off between jobs, I eventually got bored to the point that I wanted to work but on different things. I decided to do some online contracting. One site I found was TopCoder[0]. I liked the way the system was set up and they had different sorts of arrangements from bugfixes paying the first submission to pass acceptance, to longer period contests awarding 1st, 2nd, 3rd prices, etc. I only worked on things that were new/interesting to me and typically would be very keen for the first 80%, and sometimes complete (submission with a pretty good win/show/place record). My completion rate was probably less than 33%, sometimes only missing by hours. I guess the OCD in me made me finish those close-to-done ones anyway.

Unless you're very quick at what you do and can find work that suits, the hourly rate can be pretty dismal. That was when it was likely less popular, and rates may have gone down. The upsides are that the posts are well written up, challenging, and have TopCoder staff that oversees the process with a Q&A forum for each contest where questions answered, requirements clarified, materials are posted, etc.

[0] https://www.topcoder.com/

... I remember the good old days with HackHands.

It was fun to do totally random programming tasks. Probably 80% of the time it was super-easy, particularly helping college students with their CS homework. (Don't knock it, the students are agreeable and appreciative.)

The trouble is that you'd get jobs that were just insane. For instance some German guy wanted me to log into their production Microsoft SQL server and make changes. This is something I'm just barely qualified to do, don't want to take the risk of blowing up the server, don't know if he's really got permission from his supervisor to make the change, etc.

Either get a second remote job and put in minimal effort (sketchy but people do it) or invest in yourself. As a programmer, you probably have some of the best ROI for self improvement compared to most professions.