I'm not sure to what degree you can influence how a model thinks, but you can definitely hide the thinking tokens and tell the model how you want it to talk to you.

For example, the Claude web UI has an Instructions field where I have told it never to congratulate or praise me for asking questions. Earlier Copilot models used a ridiculous number of emoji and bullet lists when answering literally every prompt, I told it to knock that off and prefer detailed paragraphs in prose.

Local agents/frameworks/whatever all have their equivalents for overall user preferences.