Sometime in the last few years, Google started doing that very thing in their search results. After 1-3 seconds, sometimes a widget pops up which pushes all the search results down. I have countless times gone to click a URL after 2 seconds of searching and had it suddenly move and end up on a different website.
It's incredibly disconcerting. Because of the inconsistency, I've become hesitant and scared to click anything for the first ten seconds of loading the page. I'm being habituated by negative stimulus. Nothing has ever made me want to ditch Google search more strongly because it's now literally giving me anxiety to view the search results.
Anyone who was in charge at Google and had good design sense is long gone, and an empty-headed cargo cult remains.
P.S. I organize my bookmarks bar by favicon color without labels. Gmail was fourth, after the EFF, Youtube, and SMBC. Now I will be kicking gmail to the end of the bar with the rest of the multi-colored icons which can't be sorted and remain indistinguishable from each other. I may be a small data point but Google just effectively killed their premium placement in my bookmarks which will lead to checking my web mail less frequently.