What is a proper way to handle AdaptiveCard action on the client side using DirectLine? Should I build "value" for activity by hand?
If so, I realized that multi-select's value is handled in different way for different channels (BotFrameworkEmulator sends the values separated with commas while WebChat uses semicolons). Which format should I pick? Isn't this inconsistency a bug?
The Emulator is in a sense a form of WebChat. I don't think the inconsistency is a bug, but if you see WebChat in different places then it's likely to be different versions and may therefore have different behavior.
Fortunately your bot code is free to interpret the received values however you want it to. If your bot is likely to run on multiple channels then you may want to make your bot smart enough to account for multiple possible choice-separators. Otherwise you can just make sure your bot is looking for the right separator for the channel you want to run it on.
As far as I can tell commas are the more standard up-to-date separators, so it's probably best to go with those. But if you're making your own Direct Line client then it's ultimately up to you how you format the activities that your client sends to the bot.