No worries! Have you worked on car brakes before? Bike brakes aren't any more "black magic" than those, though again I will say they're more fiddly in my experience, because getting all the air bubbles out can be a pain sometimes. I've bled countless car brakes and it was always fairly easy with a helper to pump the pedal, but my experience with my 2 bikes has been more troublesome. I'm not sure what the problem is, considering cars have rather complex systems with multiple master cylinder reservoirs (2, for redundancy), 180 or 360-degree bends in the brakes lines, and now ABS systems, but getting all the air bubbles out of my bike systems turned out to be a bit of a black art, and it differs by caliper position (front vs rear) and hardware mfgr. The $20 brake bleed kits on Amazon are pretty good though, including all the stuff you'll need.

The nice thing about hydraulics is that, once they're set up, they're good until you need to change the pads usually, and even then the fluid is probably fine unless it's old. Rim brakes, on the other hand, need constant adjustment and fiddling just to keep them from rubbing, as the pads wear. I don't miss them one bit.

I'm in Japan. I've only checked Amazon, but I didn't see any problems getting parts there. I'd recommend looking at online sellers instead of local shops. Local shops aren't motivated to look for anything beyond what their preferred supplier has in stock.

Back in the US during Covid, I needed a new derailleur hangar because I bent mine, and wanted it quickly so I could go riding again. My local shops all said it was hard to find and expensive, and I'd have to wait a month just for them to install it (and they wouldn't sell it to me directly) for a small fortune because they said it needed to be specially bent (it didn't). So I found an online shop that had it and bought 2, got it in a few days, and installed it myself. Sorry, but after that experience, the people saying "support your LBS!" can shove it.

The other thing you should be aware of is that the exact part you're looking for may not be easily available. So if you want to replace a whole caliper, for instance, you'll probably have a much easier time finding a compatible caliper (probably a newer design) than finding another of the old one. Mfgrs are constantly updating their product lines, so it's frequently cheaper to just get something newer rather than an exact replacement, though of course there's limits here (you can't easily change from a 10-speed drivetrain to an 11-speed one, for instance, but you can easily mix-and-match different 11-speed cassettes). For hydraulic brakes, on road and hybrid bikes these days, they mostly all use the same flat-mount standard, with a few different rotor sizes.

Tektro HD-M275 front and rear. When I go online, its ali, ebay and grey market suppliers mostly, not a heap of returns from recognisable Australian bike shops.

Maybe its my bad timing, buying a 2nd had bike when it was end-of-life for one model of brake, and now it needs work, people have moved onto the next 'best thing' and I am behind "can't get the parts"

(I know one respondent disagrees and says they are both easy to fix, and easy to get. I am just reporting both what I was told and what I find when I look. "easy" is very contextually defined in both cases. It would be very easy for me to confuse myself, order the wrong bits, or manage to dismantle but never re-mantle things.)