Former teacher here, now out of teaching for 8/9ish years.
If you want a desk job, you need to decide if you want to work for a charity or non profit, or in a government role. Or if you want to step into the corporate world.
That alone will determine the sort of place you'll start looking at.
The corporate world is just any business that works for profit. Could be B2B (businesses selling to other businesses, e.g. manufacturers to retailers, suppliers to construction etc), or B2C (business to consumer). B2C are selling to the general public. In my experience, B2B can be a little slower, but not by much, and more traditional in approach (more stuffy!), and B2C is more creative and more creative freedom... but with more pressure.
Corporate jobs in B2B and B2C focus on the main areas of business: sales, marketing, HR, Finance, Operations, and IT. It's pretty much the same everywhere.
Sales suits chatty people who LIVE to build relationships with others.
Marketing suits creative types who have an analytical mindset.
HR suits the peopley people who just love to mediate between others and recruit new people to the business.
Finance suits people who like budgets and spreadsheets and numbers.
Operations varies depending on the business but if you like to be in the thick of delivering the actual product or service then this could be for you.
IT suits quiet people who like to work with tech and help others fix computer issues.
Many of these roles exist in the not for profit and charity space too.
But the big difference with a charity role is that you are under less pressure to perform according to the profit of the business. It's a different vibe. More relaxed, typically. You might be the only person doing your job role and there might be no one really checking up on you and your progress, which is nice if you don't want pressure... but may stunt your career progression long term.
Government jobs are apparently low pressure and high income roles. Two friends of mine are civil servants and can do the school run and work from home.