Your comments

"Saved search would be even better if you could manually order them so that they can act like mail folders"
Saved searches are able to be drag and dropped to reorder them. There was a regression in GLPI 10 that removed that ability, but it was re-added for the next minor release (GLPI 10.0.8). You can find the patch here:

You can sort the Queued Notification search results as you see fit and then save that as a saved search and make it the default. That would avoid you having to change the GLPI source code.

Completed for the next main release GLPI 10.1.0.

I am fairly sure this was already fixed. Have you checked the latest GLPI 10 release?

I believe users cannot close/delete their posts after 2 hours. It will need closed by a GLPI support agent (not me).

Do you have an image that shows this counter? I don't recall that being in 9.5. Is it possible you had a plugin that added it?

This is already possible by adding "Assigned to a supplier" as a hidden field in the ticket template (Templates button at top of ticket pages).

You can use tasks with the state set to TODO for this. That also means that ticket/change/problem templates can have multiple TODO tasks added. You can click the checkbox on the TODO tasks to mark them as DONE.

Tickets can be imported using the GLPI API.