Cannot Paste into chat when using Steam Remote Play

I think I just found a new problem with text copy/paste for trade. This happens when I am using Steam's Remote Play to play from a thin-client set up with my living room TV from my computer in my office.

I have confirmed what is happening. When I copy the link as found on the trade webpage while playing on my big screen downstairs, it pastes the message into my paste bin on my thin-client computer downstairs, but when I go into POE's chat and attempt to paste it with[ctrl]+[v], it pastes text from the paste bin on the computer in my office.

Steam remote play only allows access to the running game and does not allow me access to any other application (like an internet browser) on my computer in the other room so I cannot copy the Trade Whisper text into that computer's paste bin from downstairs, so therefore it seems I am unable to do any trade in POE from the thin-client in my living room when streaming the game from elsewhere.

Are there any solutions for this weird use case scenario?