At the risk of sounding like a broken record from a similar thread about Minnesota trading up, it's contingent on a team wanting to trade down.
Thanks to the NFL Draft, I think there's a misconception that if a team offers enough on a draft pick value chart that the other team would definitely trade down. In many cases, a team would rather just stay put and not risk missing out on their guy since the expected value of a garden variety 2nd rounder isn't as high as most of us like to think. NHL teams will typically trade down if they can land they guy they would have taken at their original spot.
The other factor is most of the teams picking in the top 10 probably picked up some extra 2nds/3rds at the trade deadline. And then with regards to the 2024 draft class, there's apparently a depth drop at around #20 so a high 2nd rounder might be even less appealing.
Some post-lockout examples:
2005: San Jose offered #12, #35, and another later pick to Columbus for #6 but were turned down. Sharks then completed a deal to send #12, #49, #207 to Atlanta for #8.
2006: Boston offered #5 and #37 to Washington for #4, but the Caps declined after Boston indicated that they would be taking Nicklas Backstrom.
2007: St. Louis offered #9 and #24 to Edmonton for #6; Blues wanted Jakub Voracek. But since there was a perceived tier drop after #7, Edmonton declined. St. Louis' next target after Voracek was Lars Eller who they thought would be available a few picks later. St. Louis pivoted and traded #9 to San Jose for #13, #44, and #87.
2008: Islanders traded #5 to Toronto for #7, #68, and a future 2nd. Then they traded #7 to Nashville for #9 and #40. As I remember it, Garth Snow inherited a barren farm system, so he was happy to acquire more picks.
2009: Ottawa approached Toronto about moving from #9 to #7 but they didn't get to make an offer once they said they were targeting Nazem Kadri.
2012: Garth Snow infamously channeled his inner Mike Ditka and allegedly offered all of the Islanders picks to move up from #4 to #2. Columbus declined.
2013: I think Buffalo was trying to move up from #16 to get Max Domi but were unable to find a trade partner.
2015: Toronto put out an offer (contingent on "their guy" not being available) to send #4 to Columbus for #8, #34, #38, and #58. Columbus thought the ask was too much; They had a slight preference of Noah Hanifin over Zach Werenski. They'd link up later and Toronto traded #29 to Columbus for #34 and #68.
New Jersey offered #6 to Columbus for #8, #34, and #129. Columbus declined and figured there was a good chance that Werenski would last two picks. Columbus apparently got stonewalled after asking Carolina about #5.
2017: Vegas wanted to make a splash at its first draft and walk out with Nolan Patrick at #1. New Jersey was apparently willing to trade back to #3 since at least one of Nico Hischier or Cale Makar would still be there. But Dallas was unwilling to trade back from #3 to #6. Dallas reportedly also turned down an offer from the Rangers (#7 and #21) for #3.
2019: Arizona traded #14 and #45 to Philadelphia for #11. Arizona had Victor Soderstrom in their top 5.
2021: I couldn't find any exact offers, but the Sharks pinged a couple teams about moving up for William Eklund and were ecstatic when they got him at #7. They had him #2 on their draft board.