My understanding of the modifier ような on 気がする is that it functions as a "fuzzifier". It describes the sensation as being even vaguer, tentative and ballpark-ish than 気がする by itself already implies. The exaggerated "quasi-translations" below should hopefully illustrate the nuance I'm trying to hint at:

何かを忘れた気がする。

"I have a hunch that I've forgotten something."

何かを忘れたような気がする。

"I'm experiencing a sensation that I can't quite pinpoint, but it resembles the feeling of having forgotten something -- maybe I really have forgotten something, or maybe its something else, or maybe I'm just imagining things..."

However, constructions like ような気がする are used quite often in day-to-day conversations; and you shouldn't read too much into it. In practice, I fell in tends to often be used by the speaker to cover their ass a bit in case whatever they say turns out to be nonsense.

My understanding of the modifier ような on 気がする is that it functions as a "fuzzifier". It describes the sensation as being even vaguer, tentative and ballpark-ish than 気がする by itself already implies. The exaggerated "quasi-translations" below should hopefully illustrate the nuance I'm trying to hint at:

何かを忘れた気がする。

"I have a hunch that I've forgotten something."

何かを忘れたような気がする。

"I'm experiencing a sensation that I can't quite pinpoint, but it resembles the feeling of having forgotten something -- maybe I really have forgotten something, or maybe its something else, or maybe I'm just imagining things..."

Constructions like ような気がする are used quite often in day-to-day conversations, and are often used by the speaker to casually "cover their ass" in case what they say turns out to be nonsense -- or at least to me そのような気がする...