No it wasn't. Nobody credible ever reported that Jesse had asked to be traded, just that both sides were ready to move on. There's a difference.

It might still be too early for that request to come from his side. I'm trying to stay cautious to any updates because it seems like a situation that can flip at anytime. I want him back and is among by favorite players to watch but do see more concerns now than a year ago. For his age he has an injury history that can't be ignored. Haven't seen him finish a season yet with high level of confidence seems to hit a wall that really slows him down. Could be related to the injury aspect. Those are smaller things to me and wouldn't get in the way of me signing him but I'm not Holland.

"... Puljujarvi has value, and that much of his struggles in the second half was a combination of getting COVID, being injured and then losing his confidence. I would agree. We’ve seen many players lose their confidence and it is very noticeable on the ice. Puljujarvi wasn’t close to the same player after COVID and his injury as he was to start the season.

It is important to remember Puljujarvi had 10-13-23 in the first 32 games until COVID. He returned and produced only two assists in 10 games. Then Woodcroft was hired and Puljujarvi produced 2-1-3 in four games before getting injured. He scored 2-6-8 from March 17th to the end of the season. He didn’t have much confidence making plays over the final few months. The Oilers might trade Puljujarvi, but Holland will have the same approach he had in 2019 and 2020. He won’t give him away, and will only trade him if he feels he is getting a player of similar quality in return."
- https://oilersnation.com/2022/07/04/monday-musings-dustin-schwartz-returns-trades-nhl-entry-draft-and-more/