The LLM doesn't intervene much actually, it just tells what tool to call. It's your MCP implementation that does the heavy lifting. So yeah you can always shove a key somewhere in your app context and pass it to the tool call. But I think the point of other comments is that the MCP protocol is kinda clueless about how to standardize that within the protocol itself.
I think an important thing to note is the MCP client is a distinct thing from the ‘LLM’ architecturally, though many LLM providers also have MCP client implementations (via their chat ui or desktop / cli implementations).
In general, I’d say it’s not a good idea to pass bearer tokens to the LLM provider and keep that to the MCP client. But your client has to be interoperable with the MCP server at the auth level, which is flakey at the moment across the ecosystem of generic MCP clients and servers as noted.