I see two different issues in your scenario. First, nobody timed the search, so you have no other choice than to utilize the information available to you, the estimates of time by yourself and the players in your group.
The second issue, everyone saw your ball fly into a GUR area, the tree. Without being there I can't say for sure, but you could have grounds to conclude that it was Known or Virtually Certain that the ball was lost in the GUR area, and you would deserve free relief. However, if you do conclude that the ball is lost in the GUR, and put another ball in play (by dropping it), that's the ball in play, even if you find your original within the 3-minute search period.
This is the 2020 model used maybe 3 months. Head looks brand new, always used with putter cover. This putter retails for $349.99. You can see it HERE. I am selling it for $215 shipped, that a smoking deal. I am firm on the price, so please don't PM me and offer less.
Personally, I would never view a 5 footer as a "gimme". In our game you would rarely get a putt of that length given to you unless you were completely out of a hole and we were just tired of watching you hack it around.