Hello,
You mention having problems selecting all keys in the timeline, but in the video you sent you are selecting items only in the tree.
I am not noticing abnormal behavior in your video, nor locally when I tried to reproduce your issue, because it is not expected for the keys to get selected when you click on items in the tree.
I noticed you have a filter active in the dopesheet, which may be affecting what you are able to see in the dopesheet.
If what you're trying to achieve is to select every single key in your dopesheet, you can press the spacebar twice on your keyboard, then press CTRL+A
after making sure the dopesheet is in focus, to select all of the keys.
If you want to only select a subset of bones/slots, then move all of the keys, you can do as you were doing in the video, but then click on the dopesheet (such as the dopesheet view name) to bring it in focus (it is in focus when the Dopesheet view name is underlined) then press CTRL+A
to select all of the keys currently visible in the dopesheet.
I hope this helps!