AS someone who has several Core Shell windows open at once,
GIVEN THAT my workflow often requires uploading new versions of files to servers,
AND GIVEN THAT the source files I upload are normally in different folders,
I WANT each window to present the same source folder as last time when I right-click on the ssh terminal window and choose Upload to...
SO THAT I don't have to keep changing folders.
That is something that I would setup a folder synchronization job for. I use Carbon Copy Cloner for some of my jobs in my network. CCC uses rsync over ssh so you can reach any machine you can ssh to. There is also open source tools like syncthing.net that will keep folders in sync. Resilio.com is a paid solution with a free entry level version. You can also put all remote and local machines in the same vpn mesh network using Tailscale to ensure all communication is encrypted.