@Gwen-Dragon - I created a test page. It works in Firefox (Gecko) and Edge (Chromium). It fails in Chromium browser, Google Chrome, and Vivaldi. I don't know how to proceed further on this track. Should I:
Make a change request for Vivaldi?
Plead my case with the Chromium developers?
Try to get the remote site to change their cookie parameters? (Not likely to succeed, and it wouldn't help with other sites.)
For now, I am using a four-tab tiled grid in Vivaldi. It basically works, but is fiddly. All panels have to use the same zoom scale. I have to adjust the tile sizes and scroll positions after each startup. To check for session timeout, the document in each tab reloads itself every 25 minutes. That shifts the scroll position a little each time, so eventually I have to readjust them. I'm looking into JavaScript to periodically restore the scroll positions.
2020-09-21 1617 GSHP Tile Creep.jpg
This all seems harder than it ought to be. It might help to have options to lock the zoom scale and/or scroll position and/or size of a tile (or a tab). Maybe a little padlock icon/button at the intersection of its scrollbars. That would make the panel work a bit more like an iframe (which can specify scale and offset).