Based on the intents docs, it looks like there isn’t currently an intent to change the mode of a climate entity, so you will need to set up a custom sentence in an automation with a Sentence trigger. It is also possible to do it with a custom sentence and intent script, but the automation option is easier.
Before they created the built in climate temperature intents, I created 2 custom sentences: 1) to control heat/cool & 2) to adjust temperature. as I couldn’t figure out how to differentiate between ‘set thermostat to heat/cool’ & ‘set thermostat to xx degrees’. Only quirk is I have to say ‘set thermostat to heat/cool mode’ to change operation mode.