Harry knew that his magical powers were increasing in an alarming rate from the moment he woke up in front of Dursley's door step and the reason for that was because of his soul.
Voldemort was the only living person who has a very in-depth knowledge about souls because unlike Dumbledore who gathers his knowledge from books and carful research, Voldemort research didn't worry about danger or bloodshed. He always scarified many and did extreme experiments to improve his knowledge at a fast rate to catch up to old monsters like Dumbledore
Voldemort focused more on soul research after his fifth Horcrux because his body showed instability after the fifth creation. Since there was no way back because he created his first one during his school day's he decided to move forward in the direction to improve his soul and body powers through rituals so he slaughtered many to increase his understanding of soul and body, and all that hard earned knowledge is now Harry's to use once he understands it
Harry understood that his soul is very strong as it was but after consuming Voldemort main soul, Harry's Horcrux and Harry Potter's soul it became very powerful.
I took a whole year to completely digest Voldemort memories and knowledge which was integrated into Harry and after completion, he was able to feel magic around him. Harry's capacity has reached to the level of prime Voldemort before his death and the main advantage Harry saw was that his body had two storage areas.
The first one was the magic capacity of peak Voldemort which was stored inside his soul and the second one was his own magic within his 10-year-old body which was his primary one. Soon when he becomes 11 years old, his first magic maturity will begin for his own magic.
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Usually, magic is stored inside the wizard's body and not the soul but in Harry's case he had a secondary storage inside his soul and even when he used secondary reserve it also recovered back at a fast rate
Each Wizard or Witch go through 3 stages of magic maturity and each stage improves the magic capacity of the said Wizard or Witch. With Harry's case where Voldemort's peak magic capacity was stored inside his soul as a secondary battery and his primary magic will only start to grow from his 11th birthday.
The reason why Dumbledore didn't notice Harry's secondary magic storage was because it is inside his soul. But with just magic capacity Harry knew he can't stand toe to toe with Dumbledore because even though Voldemort capacity was same as the old aged Dumbledore, Voldemort didn't fight an all-out battle with him because he knew what type of monster was the famous Albus Dumbledore.
Voldemort knew his limits and if he fought Dumbledore he would die so. He decided to improve his influence, political power, followers and gradually over take on Dumbledore with time because Dumbledore is old and his magic storage has stopped growing long back and it has start to regress as more years pass but fate played a nasty game with Voldemort in the form of prophesy and because of Harry, Voldemort main soul was no more than a secondary power battery of Harry.
Harry planed to not use his secondary magic storage unless it's necessary and decided to develop his own magic powers through his own methods he finds throughout his magic journey. He wanted to improve his skills using his own handed to find out the difference between these magic prodigies like Dumbledore, Voldemort and Grindelwald.
Harry was a genius in his previous life so he wanted to see how far can he go on his own. Harry had used wandless magic contacted a house elf of the Noble Potter Family and from then on it was a piece of cake to take over Dursley's house when he was two years old. He must have used his secondary magic reserve to contact the House elf when he was a baby without his knowledge and it made sense because it was not possible to use wandless magic to summon a House elf at that age.
Even though he knew the Dursley's where bad people he didn't make them suffer too much. He made sure that the Dursley's maintained cruel treatment towards him when he was outside with the Dursley's but it was nothing but an act to not alert Dumbledore. When they are in the house it's like they didn't know that a boy named Harry Potter lives with them because of house elf magic and he doesn't leave his room through normal way and use House elves to travel around.
End
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