He would likely be more confident. Having the powers of the Human Torch gives him a new level of strength. So he might stand up straighter and be more assertive in his actions.
In many fanfictions, Izuku adapts by relying on his heroic spirit. He sees the similarities between his world and the Spider - Verse in terms of helping people. So he starts to work with the local heroes, like Peter Parker or Gwen Stacy. He learns from them about the different threats in the Spider - Verse and how to handle them. He also tries to incorporate his own fighting style from My Hero Academia with his new spider - based powers. For instance, he might combine his One For All power with his new spider - strength for more powerful attacks. This process of adaptation is really exciting to read about as it shows Izuku's growth in a new and different environment.
His friends like Ochaco could help. She might use her zero - gravity ability to assist in handling heavy parts during the construction. Also, Iida could be there to keep things organized and on schedule with his strict sense of order.
Bakugo is often a key character. In many fanfictions, Bakugo's reaction to Izuku's evolving quirk can range from envy to begrudging respect. Their relationship is always a central focus, with Bakugo either trying to outdo Izuku or having to come to terms with Izuku's newfound power.
Izuku would probably be terrified at first. After all, he's been kidnapped by villains. But then, his hero - like determination would kick in. He might start looking for ways to escape or at least resist their plans.
All Might often appears. Since he was Izuku's mentor, in time travel scenarios, he might be the one Izuku turns to for advice or assistance. Another common character is Bakugo. Their complex relationship can be explored further in time travel stories, like if Izuku goes back in time, he might try to change how Bakugo treated him in the past.
There could be his friends like Ochaco Uraraka. She might be in a position where she's trying to understand Izuku's situation and help him. Maybe she tries to convince the people forcing Izuku to give him some space.
Ochaco Uraraka could also be a common pairing. Since she has her own insecurities and dreams in the hero world, Izuku's reality - controlling power could play a role in either helping her achieve her goals or creating new challenges for their relationship. For example, if Izuku accidentally changes something in reality that affects her family's financial situation, it could impact their relationship and how they interact.
Bakugo is often paired with Izuku. Their complex relationship from the original series can be further explored in fanfiction with Izuku's growth quirk. All Might is also a common character paired with Izuku. He could play a role in guiding Izuku to control and develop his growth quirk. Ochaco is another one. She might be involved in stories where Izuku's growth quirk affects his relationships, especially romantic ones.
All Might would probably be in it. Since he's Izuku's mentor, he could play a role in helping Izuku understand and control his time - controlling power. Maybe he has some past experience related to time powers that he shares with Izuku.