Generalize eglot-flymake-backend

Generalize eglot-flymake-backend

Loosen coupling between eglot-flymake-backend and flymake-mode.  The
flymake-mode check in 'eglot-handle-notification publishDiagnostics'
was a hack (and it wasn't even functioning correctly on M-x
eglot-shutdown/eglot-reconnect).

This should also allow eglot-flymake-backend to be driven by
diagnostic-annotating frontends other than Flymake, such as the
popular Flycheck package.

* eglot.el (eglot--managed-mode): Use eglot--report-to-flymake.
(eglot-handle-notification textDocument/publishDiagnostics): Use
eglot--report-to-flymake.

GitHub-reference: fix https://github.com/joaotavora/eglot/issues/596