Was he actually a huge Shiva bhakt or was it exaggerated to make him look good?
No, he was NOT a devotee of Lord Shiva at all. It's a made up story based on some later Interpretations or may be even propaganda.
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Far from any “Shiva Bhakti”, Ravana actually battles with Rudras on a number of occasions.
there is ONLY one instance in the entire Valmiki Ramayana, that too in Uttarakanda (7.31 CE), that Ravana worships Shiva. There is NOTHING anywhere else to even remotely suggest “Shiva Bhakti”. There is no ‘Shiva Tandava Stotram’ anywhere in the Valmiki Ramayana.
“Hearing Nandi’s words, Ravana, with his earrings trembling in his wrath, his eyes red with fury, leapt down from the Pushpaka Chariot and approaching the foot of the peak, demanded:—
“‘Who is this Shankara?’
What is the benefit of "romanticizing" an antagonist other than teaching people that look, no matter how big of a worshipper you are, how much knowledge you posses, how powerful you are - nothing matters in the end when you have stepped away from the path of Dharma and Maryada.
As per the many interpretations of Ramayana, one can definitely say he was a big Shiv bhakt, some would argue even the biggest. There's the story about him lifting the Kailash Parvat to demonstrate his power to Shiva, if he was not a bhakt then why would he do that? Then there's the live example of his bhakti as Shiv Tandav Stotram, why would he compose it for no reason?
Now it is hard to go back thousands of years in the past, and in yugs and find out the truth, but from what we read, what we hear, he definitely was a big Shiv bhakt, no doubt, and not only that but he was also a great scholar of the Vedas, he had immense knowledge, and the very essence of his story is that no matter how powerful or knowledgeable you are, adharma always comes to an end, and that arrogance has no place.