You have a really nice backer board there. They will likely be happy to mount the ONT and power supply on it.
If you can even get an enclosure, it will most likely be the indoor model. You currently have an outdoor enclosure on that old BPON ONT. It wasn't unusual for the techs to use outdoor enclosures for indoor installs a decade or so ago. Know the indoor enclosures aren't sealed. They have lots of vents, so I'm not sure it would satisfy your requirements for dust reduction. The indoor enclosures provide little more than a neat way to keep everything organized. Which doesn't seem to be a need for you, as your install is already quite neat.
The ONT is no more sensitive to dust than your router and UPS. In fact, it's probably less sensitive as it's designed for outdoor temperature and humidity extremes (in an enclosure, of course). If your basement is very dusty, you should protect all your electronics, not just the ONT.
If you really want everything in a sealed enclosure, I suggest you buy one yourself and be prepared to mount it on your board when the tech removes the old equipment. If you work with the tech and don't slow them down, they are likely to use your enclosure. If not, you can always remount everything after they leave. I wouldn't let any of this stop you from upgrading.
I've also seen pictures where the tech stuffs a GPON ONT into that BPON enclosure. These were outdoor installations and the results were not pretty, as they use zip ties to hold the GPON ONT inside the enclosure since it was designed for a completely different ONT. You could ask the tech to re-use your enclosure, but I doubt you'd like the results.
Note: To make the tech's job even easier, move that shelf out of the way so they can walk right up to the backer board. The easier you make their job the more likely they will be to work with you.