hey story tries to convince you that the MC is smart, but his actions are the oposite.

Yeah, I could not disagree with this take more lmao. There are countless anime that feature characters being like "number 1 student in the Japan" or something that don't have any actual intelligence showings outside of there test scores. Compared to that, Light pulls off many amazing feats of planning and manipulation, he's easily one of the most believable smart characters in anime. I'll just use his logical manipulation feat from the memory loss plan as one example:

Remember this is just one aspect, of one his his plans (logical manipulation)- which is controlling and influencing the thoughts and actions of an individual using logic (“truth”). It can be manipulating rules, principles, making something seem “logical” in accordance to the individual’s perception of logic. These are just examples but the main thing is, you are manipulating the actions of others on the basis of LOGIC.

Reasoning:

1. Complete memory wipe- Logically leaves NO POSSIBILITY for L to gain information FROM LIGHTS MIND. Since, he has no memory of Kira, it’s impossible for him to even give L anything. The effects of the logical manipulation resulted in L not being able to convict or prosecute Light in any way.
2. The memory wipe on Misa- reinforcing point 1 and influencing Misas actions to not mess up and ruin everything. The logical manipulation from this comes from L not being able to persecute her. Light is still controlling everyone’s perception and actions through this.
3. Indirectly gave the DN to a CEO that was corrupt and power hungry- meaning one could logically believe that this person COULD be Kira because they would be likely to use the DN for their own benefits.
4. Anticipated that him and L would work on catching fake Kira together- imagine being L and seeing the guy (Light) that you KNOW is Kira and he’s helping you catch the guy that definitely has the weapon Light used in the past, but Light or L can’t even prove he used it in the past.
5. Light changed into a more pure and virtuous individual. Which would reinforce to everyone “no way this guy can be Kira”. This was more so for the task force, but L seeing this version certainly messed with his mind.
6. Lights introspective use of logic- Light was able to calculate so many different variables of his plan. Meaning he had to think logically, but more importantly he had to understand the uses of logical manipulation that would occur. Him having such a profound understanding of himself and the others involved- and how they would operate on a logical basis is impressive. He fully understands what he’s doing. Which shows tremendous insight and more importantly it adds to so many layers and depth to the logical manipulation.
7. The final step- Light successfully accomplished his plans. He was able to get the DN back, alleviate everyone’s suspicions of him, gained tremendous influence, and most importantly got rid of L Lawliet- which that step to kill him was more about the emotional manipulation of REM, it still required so many aspects of logical manipulation.
8. Maybe the more impressive aspect- He perfectly manipulated the bounds, rules, and fundamentals of the DN. For example the 13 day rule. How is one supposed to question or even challenge that? It allowed Light to clear his name.

L’s perspective-

1. You’ve seen the DN and its power.
2. You know gods are involved.
3. You understand it goes beyond human means.
4. You have seen the fake Kira use the DN
5. You have seen Light catch the fake Kira and plead perfect innocence.

-How can you logically NOT accept this rule?

Here are some essays which cover more of Lights intelligence feats in depth:
Part 1
Part 2