Software: Zenhub https://www.zenhub.com/
Need: Agile project management for multiple projects.
Other programs I've tried: jira, Monday, clickup, trello, etc
I use scrum to manage my general productivity (not just professional work) and other programs have tended to be painful when managing multiple projects, or have been fiddly in ways I didn't need. A downside to zenhub is it's only free for public projects, so someone inclined could read through your tasks. Zenhub's main selling point is github integration, but I largely ignore that and just use it for standard issue management.
Software: Obsidian.md
Need: Knowledge management system.
Other programs I've tried: Roam, dynalist, tiddlywiki, lightweight or physical note taking systems.
If you're not using a personal knowledge management system I highly recommend you read about what they can do for you, possibly under "zettlekasten" or "digital gardening". I wish I'd started earlier. Obsidian.md is sadly closed source, but it works entirely on standard markdown with locally stored files. It has a thriving thriving plugin community supporting things like sql queries of your notes, kanban boards, and spaced repetition.
Software: Pycharm, and other jetbrains IDEs https://www.jetbrains.com/pycharm/
Need: Programming environment
Other programs I've tried: Vscode, atom, sublime, etc.
Jetbrains ides make so many things easier that I would have a pretty bad time if forced to work without them. In particular their debuggers probably save me hours of pain every week. I also appreciate the perpetual license, where any version owned for at least a year is kept for life.
Obsidian's dataview plugin might have all the database features you're looking for.
Strongly agree with sync and publish though. The free solutions I out together for each are ugly.