Instrument UI has Exemplary Title and duplicating itself

[zzylex]

Description

Instrument Midi UI got stuck on the lobby with the name of "Exemplary Window Title Here", Can't close the UI and persisted to the disconnect screen, but fixed when fully exiting. Trying to drag the UI duplicated it. After a bit, the game started to lag to the point of around <5FPS.
Reproduction

Haven't tried to recreate.
Screenshots

Additional context

I was playing a song on the guitar before about 1 second before going back to lobby, where I stopped playing the midi and put the instrument in my backpack.

[VerinSenpai]

Similar to one of the issues in #35494
I bet they're related.

[VerinSenpai]

This is replicated on the latest master.
Steps to reproduce:
Ready up and start the round.
Spawn yourself an instrument.
Play some sick tunes.
End the round.
Type restartroundnow into the console and move your cursor to your bag.
Press enter to restart to the lobby and immediately put the item in your bag.

Observe the following error in the console.
[ERRO] runtime: Caught exception in "entsys"
System.Collections.Generic.KeyNotFoundException: Entity 20217 does not have a component of type Robust.Shared.GameObjects.MetaDataComponent
at Content.Client.Instruments.UI.InstrumentBoundUserInterface.Open() in C:\Users\akika\projects\space-station-14\Content.Client\Instruments\UI\InstrumentBoundUserInterface.cs:line 45
at Robust.Shared.GameObjects.SharedUserInterfaceSystem.Update(Single frameTime) in C:\Users\akika\projects\space-station-14\RobustToolbox\Robust.Shared\GameObjects\Systems\SharedUserInterfaceSystem.cs:line 1067
at Robust.Shared.GameObjects.EntitySystemManager.TickUpdate(Single frameTime, Boolean noPredictions) in C:\Users\akika\projects\space-station-14\RobustToolbox\Robust.Shared\GameObjects\EntitySystemManager.cs:line 318

[VerinSenpai]

[ERRO] runtime: Caught exception in "entsys"
System.Collections.Generic.KeyNotFoundException: The given key '1974' was not present in the dictionary.
at System.Collections.Generic.Dictionary`2.get_Item(TKey key)
at Robust.Client.GameObjects.UserInterfaceSystem.SavePosition(BoundUserInterface bui) in C:\Users\akika\projects\space-station-14\RobustToolbox\Robust.Client\GameObjects\EntitySystems\UserInterfaceSystem.cs:line 50
at Robust.Shared.GameObjects.SharedUserInterfaceSystem.Update(Single frameTime) in C:\Users\akika\projects\space-station-14\RobustToolbox\Robust.Shared\GameObjects\Systems\SharedUserInterfaceSystem.cs:line 1099
at Robust.Shared.GameObjects.EntitySystemManager.TickUpdate(Single frameTime, Boolean noPredictions) in C:\Users\akika\projects\space-station-14\RobustToolbox\Robust.Shared\GameObjects\EntitySystemManager.cs:line 318

You also get this error if the instrument window is open when the round ends, though this issue doesn't cause the window to break on the lobby screen.

[Killerqu00]

Related: #35528
This sounds like some kind of problem with the general UI code, it seems