Hive. The original version has larger tiles, the mini version is more compact but should still work as long as it’s not too windy. Hive Carbon is worth checking out if you prefer that color scheme.
For Azul I wonder if the new Azul Mini might work better, smaller tiles but the boards have indents to keep tile in place. And much better score track.
This sounds similar to SLIME (and its fork SLY) for Common Lisp. These tools use their own protocols rather than LSP in part because they pre-date LSP but also because LSP is not a good match for everything they do. In addition to the usual LSP functionality like symbol lookup, xref and completion they also provide a very good Lisp REPL. It is easy to have the server side (called swank) running as part of an existing service which sounds a lot like what the post describes. For example I’ve used SLIME to connect to my live StumpWM sessions.