It could be the tube or the flyback. Either way it's usually a death sentence I'm sorry to tell you

Sounds like a flyback issue to me.

Basic safety and soldering skills is usually all it takes to swap out. The issue will most likely be finding a replacement. Easier to find an old CRT....

WIth it open, in a dark room, see/hear where the sound comes. It could simply be dirty anode area or the flyback itself and cleaning things up will fix it. My 32" TV had similar issues when I got it and it turned out to be caused by soot on the flyback and tube, occasionally producing a conductive path with a crack sound and momentary loss of HV.

In worst case it is bad flyback and it is not likely you can find a replacement. Cleaning it all up very properly can still help but you first should see where exactly that noise is happening.

It could just be a bit of dust/moisture from sitting in storage for a long time.

I picked up a CRT that was in good working condition, great picture, but had obviously been in storage for a loooooong time. It made a lot of snapping/popping noises when first powered on, but over the next 5-10 hours of usage the frequency of the snapping and popping decreased a lot. Now it's at the point where there might be one sharp snap (with the picture temporarily distorting) once a week or so. I did give the internals a good clean but this didn't make much difference, so my assumption is that the flyback is just a bit worn out and will eventually die.

Thanks for the replies. As I couldn't open it without removing its stand I was too reluctant to turn it on with the cover removed. I did remove dust using compressed air as well as I could.
Finally I decided to find a store nearby that still fixes CRTs and had it checked there. Took a long while, in the end it wasn't fixed, had to leave the CRTs for longer, in the end the technician said that the tube itself was broken and it was somehow tricky to diagnose. He organized another used CRT instead which he claims is in perfect condition. I got it two days ago, hopefully this one will last a bit longer.

My old Goldstar CRT that came with 386 used to make popping noise with picture being cut for a fraction of second as well. It occurred only when the monitor was very warm. The solution was to disassemble it and clean all the dust. It only happened every few months and the monitor served for many years.