We read in 2 Kgs 20:7:
Then Isaiah said, "Prepare a poultice of figs." They did so and applied it to the boil, and he [Hezekiah] recovered.
According to John J. Bimson in the New Bible Commentary:
The use of a poultice of figs for the king's skin disorder (7) is typical of the practices of ancient 'folk medicine'. It would therefore be surprising if such treatment had not been tried on Hezekiah earlier. Perhaps we should assume that it had, but that it was ineffective until Isaiah delivered God's promise of recovery.
According to The IVP Bible Background Commentary: Old Testament by Victor H. Matthews, Mark W. Chavalas, and John H. Walton:
20:7 poultice of figs. Fig cakes may have been used as condiments and for medicinal purposes at Ugarit. Both later rabbinical Jewish and classical sources (e.g., Pliny the Elder) shared the belief that dried figs had medicinal value. Poultices were sometimes used for diagnosis rather than for medication. A day or two after the poultice was applied, it would be checked for either the skin's reaction to the poultice or the poultice's reaction to the skin. One medical text from Emar prescribes the use of figs and raisins for such a process. They helped determine how the patient should be treated and whether or not he would recover.
As far as I'm aware, we don't know what specific disease Hezekiah had. But, of course, the opening verses of the chapter tell us the disease would eventually prove fatal for Hezekiah.
Hezekiah did not take his impending demise well, and "wept bitterly" (v3). The Lord responded and told Isaiah to deliver the following message to Hezekiah:
"Go back and tell Hezekiah, the ruler of my people, 'This is what the Lord, the God of your father David, says: I have heard your prayer and seen your tears; I will heal you. On the third day from now you will go up to the temple of the Lord. I will add fifteen years to your life....(2 Kgs 20:5-6a)
And Hezekiah was healed after the poultice of figs was applied to his boil(s).
If we hadn't been able to peek behind the curtains to know Hezekiah would die from his illness, as well as that it was the Lord who would spare Hezekiah's life, then we could very well have concluded ordinary medicinal remedies, i.e., the "poultice of figs," worked to effect healing for Hezekiah. However, we know the truth is God stood behind this otherwise ordinary looking medicinal remedy. Had God not granted Hezekiah's prayer, then Hezekiah would not have had an extra fifteen years of life. Had God not granted Hezekiah's prayer, then no medicine would've worked to cure Hezekiah.
Now, as far as I can tell, only Hezekiah and Isaiah knew Hezekiah should've died from his illness. And Hezekiah only knew because Isaiah told him what God told Isaiah. In addition, again as far as I can tell, only Hezekiah and Isaiah knew God had heard Hezekiah's prayer and spared Hezekiah's life. And Hezekiah again only knew because Isaiah told him what God told Isaiah. Hezekiah had to trust Isaiah's word. (Perhaps that's why Hezekiah wished for an additional sign, in spite of the prophet's word, which was God's word which Hezekiah should've trusted.)
Others like those who prepared and applied the poultice of figs may have known. But they just as well may not have known. After all, it doesn't sound like Isaiah had a compelling reason to tell anyone else God's plans for Hezekiah. So it seems plausible only Hezekiah and Isaiah would've known Hezekiah's recovery was at all a miraculous answer to prayer. It seems plausible this miracle would've been a private miracle. It seems plausible it wouldn't have been verifiable by outsiders. No one outside Hezekiah and Isaiah would've been able to rigorously examine and demonstrate it was a bona fide miracle. And, arguably, perhaps not even Hezekiah or Isaiah would've been able to do so. "All" they had was God's word.
In short, it most likely would've appeared to outsiders that Hezekiah fell sick, "a poultice of figs" was applied to him, and he was healed. On the face of it, there wouldn't have seemed to have been anything miraculous about any of it at all. There would've been at least some expectation the poultice of figs could work.