"Chat messages can't be verified" — what it means
It's not malware and nothing is broken. The warning is Minecraft's way of saying a chat message arrived without a valid cryptographic signature.
Since 1.19, every chat message you send is signed with a key tied to your Microsoft account. That signature is what makes chat reportable: it proves, mathematically, who said what. When a server relays chat whose signatures don't check out, your client flags it — "can't be verified", the "Not Secure" marker, or grayed-out messages if "Only Show Secure Chat" is on.
The twist: on a lot of servers this is deliberate. Server owners strip signatures precisely so their players' chat can't be reported to Mojang. Unsigned chat isn't a threat to you; it's chat that can't be used as evidence against whoever sent it.
If you want the warnings gone, that's a client-side job: install No Chat Reports and your client stops flagging unsigned messages (and stops signing your own). Since Minecraft 1.20.2, the server alone genuinely cannot remove that warning for you — only a client-side mod can. Server owners running the mod can also convert player messages to system messages, which vanilla clients don't flag.
Client, server, or both. Every version, hosted here.