Will my wife's absence from Thailand affect my Non O extension while she travels to the UK?

Don't affect you and not mandatory for you to join to UK

Won't affect you in the least.

There is no obligation that you travel together, you just happen to be here on an extension that is tied to hers (which only matters when your extensions come due) not that she has to be here for your extension to be valid.

Your extension is good for as long as it's good for whether the primary extension holder (that you have the trailing spouse extension from) is in the country or not

She can travel alone, you can travel alone, you guys can travel together.