Make eglot use flycheck

eglot-with-flycheck.el

    (defvar-local flycheck-eglot-current-errors nil)

    (defun flycheck-eglot-report-fn (diags &rest _)
      (setq flycheck-eglot-current-errors
            (mapcar (lambda (diag)
                      (save-excursion
                        (goto-char (flymake--diag-beg diag))
                        (flycheck-error-new-at (line-number-at-pos)
                                               (1+ (- (point) (line-beginning-position)))
                                               (pcase (flymake--diag-type diag)
                                                 ('eglot-error 'error)
                                                 ('eglot-warning 'warning)
                                                 ('eglot-note 'info)
                                                 (_ (error "Unknown diag type, %S" diag)))
                                               (flymake--diag-text diag)
                                               :checker 'eglot)))
                    diags))
      (flycheck-buffer))

    (defun flycheck-eglot--start (checker callback)
      (funcall callback 'finished flycheck-eglot-current-errors))

    (defun flycheck-eglot--available-p ()
      (bound-and-true-p eglot--managed-mode))

    (flycheck-define-generic-checker 'eglot
      "Report `eglot' diagnostics using `flycheck'."
      :start #'flycheck-eglot--start
      :predicate #'flycheck-eglot--available-p
      :modes '(prog-mode text-mode))

    (push 'eglot flycheck-checkers)

    (defun sanityinc/eglot-prefer-flycheck ()
      (when eglot--managed-mode
        (flycheck-add-mode 'eglot major-mode)
        (flycheck-select-checker 'eglot)
        (flycheck-mode)
        (flymake-mode -1)
        (setq eglot--current-flymake-report-fn 'flycheck-eglot-report-fn)))

    (add-hook 'eglot--managed-mode-hook 'sanityinc/eglot-prefer-flycheck)