Is it feasible to do any meaningful work in this field without joining a team? (e.g. as a solo hobbyist/entrepreneur)
Doing fundamental reseach is a taller order. But lots of software, tools, pipelines etc need maintainers, optimizations...
Most of the packages on bioconda (https://bioconda.github.io/) are open source. But you probably want to find a sub-field that interests you most before finding a project.
In grad school, we also had an ex-google software engineer volunteer with us one day a week. It was very impactful for many members of the lab to learn good engineering practices, and it wasn't at all like the sentiment others in this thread are expressing where engineers were "janitors".
He proceeded to completely understand hidden markov models and protein sequence alignment and was immediately hacking improvements to HMMER. However, Sean Eddy couldn't understand his optimizations (Sean has to know how HMMER works at all times) and so Bob went off and made his own tools like MUSCLE.
One of the reasons he can do this is, well, he's a programmer/math genius, and the other reason is that HMMs and protein alignments are a fairly well understood and programmable thing these days.
Still blows me away we train up all these people to be scientists when there are no jobs for them in that role.