Code change:
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This probably can be generalized if the code is written carefully enough.
Do you mean, we should handle other types like which may use with a closure?
I know nothing about the internals of rustc diagnostics but a general way would be to check if a similar method in name accepts a closure and suggest that first, if nothing similar can be found then suggest calling the closure
I mean something more like what is suggesting, where you check if exists whose signature is compatible with a closure. But that requires doing a method probe, then doing some delicate logic to check argument compatibility.

Related discussion:
text: } } <ins> /// issue #102320, for `unwrap_or` with closure as argument, suggest `unwrap_or_else` /// FIXME: currently not working for suggesting `map_or_else`, see #102408 pub(crate) fn suggest_else_fn_with_closure( &self, err: &mut Diagnostic, expr: &hir::Expr<'_>, found: Ty<'tcx>, expected: Ty<'tcx>, ) -> bool { let Some((_def_id_or_name, output, _inputs)) = self.extract_callable_info(expr, found) else { return false; }; if !self.can_coerce(output, expected) { return false; } let parent = self.tcx.hir().get_parent_node(expr.hir_id); if  let Some(Node::Expr(call_expr)) = self.tcx.hir().find(parent) && let hir::ExprKind::MethodCall( hir::PathSegment { ident: method_name, .. }, self_expr, args, .., ) = call_expr.kind && let Some(self_ty) = self.typeck_results.borrow().expr_ty_opt(self_expr) { let new_name = Ident { name: Symbol::intern(&format!("{}_else", method_name.as_str())), span: method_name.span, }; let probe = self.lookup_probe( expr.span, new_name, self_ty, self_expr, ProbeScope::TraitsInScope, ); // check the method arguments number if let Ok(pick) = probe && let fn_sig = self.tcx.fn_sig(pick.item.def_id) && let fn_args = fn_sig.skip_binder().inputs() && fn_args.len() == args.len() + 1 { err.span_suggestion_verbose( method_name.span.shrink_to_hi(), &format!("try calling `{}` instead", new_name.name.as_str()), "_else", Applicability::MaybeIncorrect, ); return true; } } false } </ins> /// Checks whether there is a local type somewhere in the chain of /// autoderefs of `rcvr_ty`. fn type_derefs_to_local(