Key Binds do not allow Modifier + Modifier combination

[KostromDan]

Minecraft Version: {was able to reproduce on 1.20.1, 1.21.1, 1.21.4}

Forge Version: {47.4.0, 52.1.0, 54.1.2}

Steps to Reproduce:

1. Open Options -> Controls -> Key Binds
2. Try to set LShift + LCtrl keybind for Sneak
3. Only last key saves. For this keybind: LCtrl

Description of issue:
On 1.19.2 all worked fine. On 1.20.1 and later we can't set this keybind. Only last key saves.
@LexManos tried to fix this on Discord, but we found some bugs in that solution which unfixable by easy way.
Conversation:
https://discord.com/channels/1129059589325852724/1129095235889270844/1345137142808186992
https://discord.com/channels/1129059589325852724/1129095235889270844/1345145682306007081
https://discord.com/channels/1129059589325852724/1129095235889270844/1345215593649016923
https://discord.com/channels/1129059589325852724/1129095235889270844/1345367278228607057

[Fealtous]

Replicated on 1.20.1 and 1.21.10, likely affects all versions. Modifier key state appears to be getting stuck "held" when pressed at the same time as another key. Opening any screen resets it properly.