Cleanup the flymake 26.1 hack slightly

Cleanup the flymake 26.1 hack slightly

* eglot.el (eglot-handle-notification): Use proper flymake
diagnostic types.
(eglot-code-actions): Use eglot--diag-data.
(eglot--make-diag, eglot--diag-data): New aliases to
`flymake-diagnostic-data' and `flymake-make-diagnostic'.
(eglot-error eglot-warning eglot-note)
(dolist eglot-error eglot-warning eglot-note): put
flymake-overlay-control in these.
(eglot-error eglot-warning eglot-note): put corresponding
flymake-category.
(horrible hack at the end): Move the Flymake 26.1 hack here.