Many chat systems support "/me" actions, as IRC was a familiar chat system long before all the new trendy replacements. Generally, I would think that "advanced" users would expect the ability to use /me to perform an action/emote in a way which makes sense for the system they are using, these days. (I discovered the lack by using it without realizing there was no support.)
As noted in the XMPP XEP-0245, the display should be obvious that it is user-initiated text. As a notable example of failure, Steam introduced /me support in their chat which wasn't "different" and as a result, users were able to make their actions look like system-generated text (hilarity did not ensue, but scams did).
A simple approach used by Discord is to just italicize the line of input (it looks like it's done to the input when it's received), as it's unlikely that people will do additional Markdown in an action (especially italics). This, however, is not accessibility friendly (turn on text-to-speech in Discord and you can quickly tell that actions/emotes are impossible to discern from regular chat). Maybe it'd be more accessibility friendly with bold + italics (via <strong> plus <em>) as some (maybe most now) screen readers are smart enough to read that sort of text with different intonation.
- https://support.discordapp.com/hc/en-us/articles/210298617-Markdown-Text-101?page=3#comments (The comments have fail-ish permalinks. If no reference to /me is found, look at higher numbered pages.)