How to call custom function outside from the admin page?

Out of context, it is hard to say anything definitive. There is a lot of information missing.

If you saved an Array to the $wpdb->options table (add_option or update_option) then get_option will return an Array. If you saved a string, it will return a string. If you want a string then you are saving the option incorrectly, but you haven’t posted the code that saves this value.

As far as $options['custom_logo'] being correct, without knowing how the $options array was created I don’t know what to say.

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