Can I upgrade my High Sierra 10.13.6 to Monterey 12.6.2 without upgrading to Mojave, Catalina, Big Sur?

If it qualifies, then yes according to Apple, make certain you have a good backup or two...

App Store says Compatibility 10.9 or later...

https://apps.apple.com/us/app/macos-monterey/id1576738294

macOS Monterey is compatible with these computers - Apple Support

• iMac – all models from late 2015, iMac 16,1 – 20,2
• iMac Pro – all models, iMac Pro 1,1
• MacBook & MacBook Retina – all models from early 2016, MacBook 9,1 – 10,1
• MacBook Pro – all models from early 2015, MacBook Pro 12,1 – 17,1
• MacBookAir – all models from early 2015, MacBook Air 7,1 – 10,1
• Mac Mini – all models from 2014, Mac Mini 7,1 – 9,1
• Mac Pro – all models from 2013, Mac Pro 6,1 – 7,1

TM is sometimes OK, I prefer Carbon Copy Cloner...

http://www.bombich.com/software/ccc.html

Which makes a bootable copy that you can test before you need it.:)