Trying to find a FC-M371 crank on line but no luck for my part of the world (Australia, New Zealand, Pacific Islands)

That is a standard square taper BB, so an square taper BB with suitable sized chain rings will replace it. While 9 speed would be ideal, if the best chainring match you can find is 8speed it will work reasonably well.

As far as chain ring sizes, you do not need to stick with 44/32/22. If you go larger than 44, you might need to lengthen the chain. If you increase the difference between the 44 and 22 (22), you may have problems getting it to work well.

A suitable low cost replacement might be FC-M311, which is commonly 22/32/42 - a slightly lower top gear.

Without offering recommendations, Wiggle and Chain Reaction in the UK happily supply into NZ (as long as its not Shimano) , along with JensonUSA in the US. You LBS will be able to source a suitable replacement very easily, and unless you have access to a crank puller, probably cheaper to get them to install it.

There are in the latest Shimano catalogue these 44-32-22 cranks:

• FC-M371 - square taper, riveted chainrings, 9-speed
• FC-MT101 - ditto
• FC-MT210-3, riveted, HT2 9-speed
• FC-T4060 - removable chainrings, HT2 9-speed
• FC-T4010 - removable, Octalink 9-sped
• FC-T3010 - square taper, removable chainrings, 9-speed

In general, you might well want to replace your BB, and if you're doing so the best option would probably be to go HT2, in that square taper is fine but Shimano are making progressively lower quality (cheaper) square taper BBs, and quality third party BBs will be expensive. Octalink is dead and will be combined to the trash can of history soon enough, so ignore that as you don't already have it.

It's very cheap and easy to remove your crankset, a crank puller is like $3 from China.

https://www.aliexpress.com/item/4000004797608.html

or $5 for a slightly fancier one with a handle

https://www.aliexpress.com/item/1005001375554955.html

Unfortunately removing the bottom bracket can be more challenging and you will want to buy a branded tool. However if your bottom bracket does need replacement then it's not significantly more expensive to replace it with a HT2 model.

This is the tool to remove an Octalink or Square Taper BB

Whereas a cheap $5 tool like this will do for HT2

https://www.aliexpress.com/item/32988218792.html