I don't get this whole asset with no value term that gets lumped on every player that signs a contract extension. For elite players that simply isn't true. If their health and/or performance craters then sure they have no trade value, but elite players in their prime for teams actually trying to win have plenty of value. If you sign Giles for a reasonable somewhat team friendly extension (which may be possible due to his stated desire to stay in Toronto) and the team ends up being terrible in the first half, then there is no reason you can't move him to a different team at the trade deadline, he will still have plenty of trade value. Sure if his arm falls off then you have a dead asset, there is always this risk in any kind of long term contract with a reliever.
This isn't the same situation as it was with Stroman at this point. Stroman had far more trade value as a starter with 1.5 years of control than Giles does as a reliever with only 1 year of control going forward. Stroman returned 2 top 100'ish prospects, with so little control remaining with Giles by the trade deadline you might struggle to get back even 1 top 100 player. You almost certainly wouldn't want to offer a qualifying offer to Giles in case he decided to take it. If you could have moved Giles at the trade deadline for a good return then that would have been the prime opportunity to do so. I do wonder what the Yankees offer looked like at the time, given that Giles was having issues pitching on back to back days.
The team has potentially added upwards of 10+ wins in free agency to a team that was close to .500 since Bichette was called up. This isn't the same team that was trending towards the franchise's worst ever record in the first half, it is now a team that showed enough forward momentum that the front office felt the time was right to start improving the 25 man roster, and not simply collecting assets. At some point keeping your best players to provide present value makes more sense than worrying about future value. If the return for Giles isn't a clear win vs. the value he provides on the field for the Jays, then I would argue it is better to hang onto him.