I would do it via a SyncVar of type string on the object
I would then have the clients notify the server of what value should be applied via a command e.g.
CmdSetStringValue(string data);
The server will take that data confirm its okay to apply and set it to the SyncVar e.g.
[SyncVar] public string messageData;
then in the update on the script all you need to do is
myTextField.text = messageData;
A better place to ask this sort of Mirror specific question is the Mirror discord forum ... you can find a link to it on the Mirror store page.
I would then have the clients notify the server of what value should be applied via a command e.g.
CmdSetStringValue(string data);
The server will take that data confirm its okay to apply and set it to the SyncVar e.g.
[SyncVar] public string messageData;
then in the update on the script all you need to do is
myTextField.text = messageData;
A better place to ask this sort of Mirror specific question is the Mirror discord forum ... you can find a link to it on the Mirror store page.