Similarly To
In The Same Way As, Like, As If
adverb
You learned 様 is a "formal name ender," but it can also mean manner. When you attach this to another noun with の and add に on the end to make it an adverb, you can describe something that's being done similarly to or in the same way as something else. In other words, something about it is just like that other thing — almost as if they were one and the same!
Even though this word isn't a compound, 様 actually uses the on'yomi here. Since you didn't learn the on'yomi with the kanji, here's a mnemonic to help you out:
Many foods are made similarly to yogurt (よう): kefir, skyr, lassi… The list goes on. What's that? Those are just subcategories of yogurt, you say? No, no, no. They're made in the same way as yogurt and they taste a lot like yogurt, but they're not yogurt. Yogurt stands alone.
昨日の台風がウソの様に晴れてるね。
It's so sunny — almost like yesterday's typhoon didn't really happen.
うちのWiFiは光の様に速い。
Our Wi-Fi is as fast as light.
彼は初めてのデートに王子の様に馬に乗って現れたの。
He showed up for our first date riding a horse, as though he were a prince.