[BUG] Multiple messages can be sent while the first message is still processing

[SamvelSimonyan]

Steps to reproduce:

1. Open the agent or pipeline interface.
2. Send a message.
3. While the message is processing (send button changes to "Stop"), type another message and press Enter.

Actual results:

• The second message is sent while the first message is still processing.

2025-10-01_12h01_41.mp4

Expected results:

• The application should prevent sending additional messages while the first message is still processing.

[HawkQing1]

@SamvelSimonyan the sending has been disabled if it's streaming. Please verify it on dev.

[epamLDadayan]

Verified on DEV env

[epamLDadayan]

Verified on Stage env