Though I may be arriving a bit tardy, here is some sample code that has been thoroughly tested for functionality. I recently formulated a similar request for requiring an exported variable of type StorybookDocumentation with the same objective in mind.

The key idea behind this approach involves creating a custom rule that:

1. Begins from the Program root node and meticulously scans all tokens to identify export-related tokens (in my scenario, I opted for named exports, but by tweaking the logic slightly, default exports can also be targeted).
2. Once the selection narrows down to only exported variables and their types, they are grouped into an array of [identifier, type] pairs.
3. Subsequently, it is ensured that at least one of these pairs corresponds to an exported variable of the correct name and type; otherwise, an issue is raised.

import { ESLintUtils, TSESTree } from '@typescript-eslint/utils';


const arePriorTokensExportConst = (index: number, tokens: TSESTree.Token[]) => {
    const previousTokenIsConst = tokens[index - 1]?.value === 'const';
    const previousPreviousTokenIsExport = tokens[index - 2?.value === 'export';
    const isNamedExport = previousTokenIsConst && previousPreviousTokenIsExport;
    return isNamedExport;
};
export const requireStorybookDocumentation = ESLintUtils.RuleCreator.withoutDocs({
    create(context) {
        return {
            Program(program) {
                const namedExports = context.sourceCode.tokensAndComments
                    .filter((token, currentIndex, tokens) => {
                        if (token?.type !== 'Identifier') {
                            return false;
                        }
                        const isNamedExport = arePriorTokensExportConst(currentIndex, tokens);
                        const isTypeForNamedExport =
                            tokens[currentIndex - 1?.value === ':' &&
                            arePriorTokensExportConst(currentIndex - 2, tokens);
                        return isNamedExport || isTypeForNamedExport;
                    })
                    .reduce<TSESTree.Token[][]>((acc, cur, index) => {
                        if (index % 2 === 0) {
                            acc.push([cur]);
                            return acc;
                        }
                        acc[acc.length - 1].push(cur);
                        return acc;
                    }, []);

                if (
                    !namedExports.some(namedExport => {
                        const [identifier, identifierType] = namedExport;
                        return (
                            identifierType?.value === 'StorybookDocumentation' && identifier?.value === 'Documentation'
                        );
                    })
                ) {
                    context.report({
                        messageId: 'require-storybook-documentation',
                        node: program,
                    });
                }
            },
        };
    },
    meta: {
        docs: {
            description: 'Function Component files should export a Storybook documentation configuration',
        },
        messages: {
            'require-storybook-documentation': 'Define and export a StorybookDocumentation object named Documentation',
        },
        type: 'suggestion',
        schema: [],
    },
    defaultOptions: [],
});

export default {
    'require-storybook-documentation': requireStorybookDocumentation,
}cater to Record<string, ESLintUtils.RuleModule<any, any>>;

In addition, comprehensive tests have been included to confirm its expected behavior

import { RuleTester } from '@typescript-eslint/rule-tester';
import { describe, after, it } from 'mocha';
import { requireStorybookDocumentation } from '../rules';
RuleTester.afterAll = after;
RuleTester.describe = describe;
RuleTester.it = it;
RuleTester.itOnly = it.only;

const ruleTester = new RuleTester({
    parser: '@typescript-eslint/parser',
    parserOptions: {
        project: './tsconfig.json',
        ecmaFeatures: { jsx: true },
        tsconfigRootDir: __dirname,
    },
});

ruleTester.run('my-rule', requireStorybookDocumentation, {
    valid: [
        {
            code: `
    import { FunctionComponent } from 'react';
    import { StoryObj, Meta } from '@storybook/react';

    type StorybookDocumentation<TComponent extends FunctionComponent, TDefinedStories> = {
        Meta: Meta<TComponent>,
        Stories: Record<TDefinedStories, StoryObj<TComponent>>
    };

    export const MyComponent: FunctionComponent = () => <h1>Hello World!</h1>;
    export const Documentation: StorybookDocumentation<typeof MyComponent, 'Primary'>  = {
        Meta: {
            component: MyComponent,
        },
        Stories: {
            Primary: {}
        }
    };
`,
        },
    ],
    invalid: [
        {
            code: `
        import { FunctionComponent } from 'react';
        export const MyComponent: FunctionComponent = () => <h1>Hello World!</h1>;
    `,
            errors: [{ messageId: 'require-storybook-documentation' }],
        },
    ],
});