I already have experience with Extended Script Toolkit but want to develop dockable plugins and I believe it can only be achieved with Adobe UX Developer Tool however there is no option in Playground to connect to Illustrator 2024.
So the "UX" Developer Tool you've screencaptured here is actually the "UXP Developer Tool". UXP is the Unified Extensibility Platform, a modern JavaScript environment. At the time of this writing, only Photoshop, InDesign, and Adobe XD support UXP. Illustrator does not have UXP adoption on their roadmap currently.
If you're still able to run ExtendScript Toolkit you can keep using it to develop for Illustrator. If not, there's a VS Code plugin for debugging ExtendScript. Note that on M1 and M2 macs you'll need to run that in Rosetta 2 mode.
🤔 🤔 Were you previously able to create dockable palettes or is this something you're attempting for the first time? ... I think in CEP people call them "panels".